A345750 E.g.f.: Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k).

1, 1, 2, 9, 49, 310, 2521, 25557, 290550, 3555041, 48104901, 741103946, 12825399313, 240202011881, 4747281446090, 98808864563065, 2194031697420057, 52582450760730398, 1357237338948268649

Offset: 0

Author

Seiichi Manyama, Jun 26 2021

Keywords

• nonn

Comments

Stirling transform of A168243.

Links

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

Crossrefs

Cf. A048272, A048993, A168243, A305550, A305987, A345749, A345751.

Programs

Mathematica

max = 18; Range[0, max]! * CoefficientList[Series[Product[(1 + (Exp[x] - 1)^k)^(1/k), {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Jun 26 2021 *)

PARI

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

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, -sumdiv(k, d, (-1)^d)*(exp(x)-1)^k/k))))

Formula

E.g.f.: exp( Sum_{k>=1} A048272(k) * (exp(x) - 1)^k / k ).

a(n) = Sum_{k=0..n} Stirling2(n,k) * A168243(k).