A209306 Binomial self-convolution of sequence k -> A209305(k+1).

1, 6, 52, 608, 9000, 161320, 3395384, 82067848, 2239857464, 68123898696, 2284557569272, 83741888125064, 3330861429420984, 142875672420718024, 6574169480181294200, 322998830024467434760, 16876498518902786900792, 934400728689236533139016

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.

Programs

Mathematica

(* Generating series *)
  A[x_] := InverseErf[(2 Exp[x] - 2 + Exp[1] Sqrt[Pi] Erf[1])/(Exp[1] Sqrt[Pi])];
CoefficientList[Series[A'[x]^2, {x, 0, 20}], x] Table[n!, {n, 0, 20}]
(* Recurrences *)
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[b[n], {n, 0, 100}]

Formula

a(n) = Sum_{k=0..n} C(n,k)*b(k+1)*b(n-k+1), where b(n) = A209305(n).

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