A351515 Expansion of e.g.f. (exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)^2 / 2.

1, 15, 215, 3325, 56605, 1060780, 21772595, 486459105, 11760431325, 305942552245, 8521928511915, 253041654671949, 7977871631560394, 266128899746035160, 9363456107172891499, 346487270686107589124, 13450341325170239245308, 546470289216642540029570

Offset: 2

Author

Seiichi Manyama, Feb 12 2022

Keywords

• nonn

Crossrefs

Column 2 of A039813.

Cf. A000357, A000558, A351513, A351514.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)^2/2))

PARI

T(n, k) = if(k==0, n<=1, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
a(n) = sum(k=1, n-1, binomial(n-1, k)*T(k, 5)*T(n-k, 5));

Formula

a(n) = Sum_{k=1..n-1} binomial(n-1,k) * A000357(k) * A000357(n-k).