Template:Infobox combinatorial classes

{{{notation}}}

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Usage

The Template:infobox combinatorial classes generates a right-hand side infobox, based on the specified parameters. To use this template, copy the following code in your article and fill in as appropriate:

{{{name}}} ({{{notation}}})

{{{intro}}}
Parameters	{{{parameters}}}
Support	{{{support}}}
$n$-th element	{{{nth_element}}}
Asymptotic	{{{asymptotic}}}
Ordinary generating function	{{{OGF}}}
Exponential generating function	{{{EGF}}}
Poisson generating function	{{{PGF}}}
Lambert series	{{{LS}}}
Bell series	{{{BS}}}
Dirichlet series generating function	{{{DGF}}}
Polynomial sequence generating function	{{{PSGF}}}

{{Infobox combinatorial classes
| name        = 
| notation    =
| intro       =
| parameters  =
| nth_element =
| asymptotic  =
| support     =
| OGF         =
| OGF radius  =
| EGF         =
| EGF radius  =
| PGF         =
| PGF radius  =
| LS          =
| LS radius   =
| BS          =
| BS radius    =
| DGF         =
| DGF radius  =
| PSGF        =
| PSGF radius =
}}

Parameters

• name — Name at the top of the infobox; should be the name of the sequence, without the word sequence. (e.g. "Fibonnacci", "Factorials")
• notation — How the sequence (or its $n$-th element) is usually denoted. For example, $n!$ for the sequence of factorials.
• parameters — parameters of the sequence family.
• support — Where the sequence is defined and non-zero. (e.g. it is the place to state that a sequence has only value at even position, or at prime positions.)
• nth element — The place to give the exact value of the $n$-th element of the sequence. (e.g. for fibonnaci number, it would be ${\frac {1}{\sqrt {5}}}\left(\left({\frac {1+{\sqrt {5}}}{2}}\right)^{n}+\left({\frac {1-{\sqrt {5}}}{2}}\right)^{n}\right)$)
• asymptotic — A function with the same domain than the sequence, which is asymptotically equivalent to it. (e.g. for fibonnaci number, it would be ${\frac {1}{\sqrt {5}}}\left(\left({\frac {1+{\sqrt {5}}}{2}}\right)^{n}\right)$)
• OGF, EGF, PGF, LS, BS, DGF, PSGF are defined as in the page Generating function
• OGF radius, EGF radius, PGF radius, LS radius, BS radius, DGF radius, PSGF radius the radius of the previously defined functions

TemplateData

See a monthly parameter usage report for Template:Infobox combinatorial classes in articles based on its TemplateData.

TemplateData for Infobox combinatorial classes

No description.

Template parameters[Edit template data]

This template prefers inline formatting of parameters.

Parameter		Description	Type	Status
box_width	box_width	no description	Unknown	optional
Name	name	Name at the top of the infobox; should be the name of the sequence, without the word sequence Example Fibonnacci	Unknown	optional
notation	notation	no description	Unknown	optional
intro	intro	no description	Unknown	optional
parameters	parameters	no description	Unknown	optional
support	support	Where the sequence is defined and non-zero. Example The even numbers. The prime numbers	Unknown	optional
nth element	nth element	no description	Unknown	optional
asymptotic	asymptotic	A function with the same domain than the sequence, which is asymptotically equivalent to it. Example <math>\frac{1}{\sqrt5}\left(\left(\frac{1+\sqrt 5}{2}\right)^n\right)</math> for Fibonnacci	Unknown	optional
OGF	OGF	The ordinary generating function of the sequence	Unknown	optional
its radius	radius_OGF	radius of convergence of the OGF Example 1	Number	optional
EGF	EGF	The exponential generating function of the sequence	Unknown	optional
radius_EGF	radius_EGF	the radius of convergence of the EGF	Unknown	optional
PGF	PGF	The poisson generating function of the sequence	Unknown	optional
radius_PGF	radius_PGF	the radius of convergence of the PGF	Unknown	optional
LS	LS	The Lambert series of the sequence	Unknown	optional
radius_LS	radius_LS	the radius of convergence of the LS	Unknown	optional
BS	BS	The Bell series of the sequence	Unknown	optional
radius_BS	radius_BS	the radius of convergence of the BS	Unknown	optional
DGF	DGF	The Dirichlet series generating functions of the sequence	Unknown	optional
radius_DGF	radius_DGF	the radius of convergence of the DGF	Unknown	optional
PSGF	PSGF	The Polynomial Sequence Generating Function of the sequence	Unknown	optional
radius_PSGF	radius_PSGF	the radius of convergence of the PSGF	Unknown	optional

The above documentation is transcluded from Template:Infobox combinatorial classes/doc. (edit | history)
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No description.

Template parameters[Edit template data]

This template prefers inline formatting of parameters.

Parameter		Description	Type	Status
box_width	box_width	no description	Unknown	optional
Name	name	Name at the top of the infobox; should be the name of the sequence, without the word sequence Example Fibonnacci	Unknown	optional
notation	notation	no description	Unknown	optional
intro	intro	no description	Unknown	optional
parameters	parameters	no description	Unknown	optional
support	support	Where the sequence is defined and non-zero. Example The even numbers. The prime numbers	Unknown	optional
nth element	nth element	no description	Unknown	optional
asymptotic	asymptotic	A function with the same domain than the sequence, which is asymptotically equivalent to it. Example <math>\frac{1}{\sqrt5}\left(\left(\frac{1+\sqrt 5}{2}\right)^n\right)</math> for Fibonnacci	Unknown	optional
OGF	OGF	The ordinary generating function of the sequence	Unknown	optional
its radius	radius_OGF	radius of convergence of the OGF Example 1	Number	optional
EGF	EGF	The exponential generating function of the sequence	Unknown	optional
radius_EGF	radius_EGF	the radius of convergence of the EGF	Unknown	optional
PGF	PGF	The poisson generating function of the sequence	Unknown	optional
radius_PGF	radius_PGF	the radius of convergence of the PGF	Unknown	optional
LS	LS	The Lambert series of the sequence	Unknown	optional
radius_LS	radius_LS	the radius of convergence of the LS	Unknown	optional
BS	BS	The Bell series of the sequence	Unknown	optional
radius_BS	radius_BS	the radius of convergence of the BS	Unknown	optional
DGF	DGF	The Dirichlet series generating functions of the sequence	Unknown	optional
radius_DGF	radius_DGF	the radius of convergence of the DGF	Unknown	optional
PSGF	PSGF	The Polynomial Sequence Generating Function of the sequence	Unknown	optional
radius_PSGF	radius_PSGF	the radius of convergence of the PSGF	Unknown	optional