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A209307 Binomial self convolution of sequence A209305. 2
1, 2, 8, 52, 492, 6172, 96572, 1810940, 39585980, 988367804, 27750071036, 865420762876, 29680685363772, 1110252095824444, 44984193111861116, 1962563143587356540, 91727727493033914044, 4572606297018521071292, 242169416254095528953852 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..375

FORMULA

E.g.f.: A(x)^2, where A(x) is the e.g.f of the sequence A209305.

MATHEMATICA

(* Expansion of the generating series *) CoefficientList[Series[(InverseErf[(2Exp[x]-2+Exp[1]Sqrt[Pi]Erf[1])/(Exp[1]Sqrt[Pi])])^2, {x, 0, 40}], x]Table[n!, {n, 0, 40}]

(* Recurrence *)

a[n_] := a[n] = a[n-1]+2Sum[Binomial[n-2, k]a[k]b[n-2-k], {k, 0, n-2}];

a[1] = 1;

a[0] = 1;

b[n_] := Sum[Binomial[n, k]a[k+1]a[n-k+1], {k, 0, n}];

Table[Sum[Binomial[n, k]a[k]a[n - k], {k, 0, n}], {n, 0, 12}]

CROSSREFS

Cf. A209305, A209306.

Sequence in context: A089467 A195192 A103239 * A323843 A132228 A305004

Adjacent sequences:  A209304 A209305 A209306 * A209308 A209309 A209310

KEYWORD

nonn

AUTHOR

Emanuele Munarini, Jan 18 2013

STATUS

approved

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Last modified July 31 12:29 EDT 2021. Contains 346373 sequences. (Running on oeis4.)