A351514 Expansion of e.g.f. (exp(exp(exp(exp(x)-1)-1)-1)-1)^2 / 2.

1, 12, 136, 1650, 21904, 318521, 5051988, 86910426, 1612648066, 32107793135, 682724688430, 15439016490989, 369914992674530, 9359103270641290, 249292192469843244, 6971850327184526783, 204215496402215939638, 6251233458455082035922

Offset: 2

Author

Seiichi Manyama, Feb 12 2022

Keywords

• nonn

Crossrefs

Column 2 of A039812.

Cf. A000307, A000558, A351513, A351515.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(exp(x)-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, 4)*T(n-k, 4));

Formula

a(n) = Sum_{k=1..n-1} binomial(n-1,k) * A000307(k) * A000307(n-k).