A345757 E.g.f.: Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k!).

1, 1, 2, 8, 34, 137, 614, 3754, 25449, 82747, -1523792, -34833005, -335209288, 194665837, 59685834069, 715582325511, -10186972407657, -584687267399246, -10975484551366964, 8845584310341044, 8145484883568515927, 330326712925212377392, 7816903733527799885488

Offset: 0

Author

Seiichi Manyama, Jun 26 2021

Keywords

• sign

Comments

Stirling transform of A298906.

Links

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

Crossrefs

Cf. A048993, A298906, A345756, A345758.

Programs

PARI

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

Formula

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

a(n) = Sum_{k=0..n} Stirling2(n,k) * A298906(k).