A351513 Expansion of e.g.f. (exp(exp(exp(x)-1)-1)-1)^2 / 2.

1, 9, 75, 660, 6288, 65051, 728556, 8792910, 113805204, 1572387410, 23094192960, 359209182397, 5896792771795, 101854538628396, 1846058978130172, 35021271971160507, 693843099578350329, 14326635965967487711, 307729547549467823822, 6864250658908517748384

Offset: 2

Author

Seiichi Manyama, Feb 12 2022

Keywords

• nonn

Crossrefs

Column 2 of A039811.

Cf. A000258, A000558, A351514, A351515.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(x)-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, 3)*T(n-k, 3));

Formula

a(n) = Sum_{k=1..n-1} binomial(n-1,k) * A000258(k) * A000258(n-k).