A173218 G.f.: A(x) = Sum_{n>=0} (1 + x)^(n^2+n) / 2^(n+1).

1, 4, 50, 1040, 30300, 1135080, 51972668, 2812429632, 175606496520, 12426817517920, 982846762742416, 85916923493646752, 8225856593959648696, 856044724445883011520, 96213518828394481754400

Offset: 0

Author

Paul D. Hanna, Mar 05 2010

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A173217, A173219.

Programs

Mathematica

Table[Sum[StirlingS1[n, j] * Sum[Binomial[j, s] * HurwitzLerchPhi[1/2, -j - s, 0], {s, 0, j}], {j, 0, n}] / (2*n!), {n, 0, 20}] (* Vaclav Kotesovec, Oct 08 2019 *)

PARI

{a(n)=local(A=sum(m=0,n^2+100,(1+x +O(x^(n+2)))^(m*(m+1))/2^(m+1)));round(polcoeff(A,n))}

Formula

a(n) ~ 2^(2*n) * n^n / (2^(log(2)/8) * log(2)^(2*n+1) * exp(n)). - Vaclav Kotesovec, Oct 08 2019