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

Author

Emanuele Munarini, Jan 18 2013

Keywords

• nonn

Links

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

Crossrefs

Cf. A209305, A209306.

Programs

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}]

Formula

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