A345756 E.g.f.: Product_{k>=1} 1/(1 - (exp(x) - 1)^k)^(1/k!).

1, 1, 4, 20, 132, 1057, 10036, 110168, 1369395, 19009207, 291638340, 4898978911, 89387432140, 1760380295559, 37222139393757, 841009071062929, 20219172890524757, 515336552717107810, 13879978696592456136, 393920374851547833518, 11749388855614114735431

Offset: 0

Author

Seiichi Manyama, Jun 26 2021

Keywords

• nonn

Comments

Stirling transform of A209902.

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Stirling Transform

Crossrefs

Cf. A048993, A140585, A209902, A345757, A345758.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(exp(x)-1)^k)^(1/k!))))

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, (exp((exp(x)-1)^k)-1)/k))))

Formula

E.g.f.: exp( Sum_{k>=1} (exp((exp(x) - 1)^k) - 1)/k ).

a(n) = Sum_{k=0..n} Stirling2(n,k) * A209902(k).