A209307 Binomial self-convolution of sequence A209305.

1, 2, 8, 52, 492, 6172, 96572, 1810940, 39585980, 988367804, 27750071036, 865420762876, 29680685363772, 1110252095824444, 44984193111861116, 1962563143587356540, 91727727493033914044, 4572606297018521071292, 242169416254095528953852

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