A345758 E.g.f.: Product_{k>=1} (1 - (exp(x) - 1)^k)^(1/k!).

1, -1, -2, -2, 4, 63, 448, 2490, 14733, 109151, 790418, 5861623, 91442844, 1857444743, 27708811583, 336714649323, 6016551711313, 167673369006642, 4183443404331446, 82140898773966502, 1493427665082817617, 37403762698805913754, 1340432910567030307828

Offset: 0

Author

Seiichi Manyama, Jun 26 2021

Keywords

• sign

Comments

Stirling transform of A345762.

Links

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

Crossrefs

Cf. A048993, A345756, A345757, A345762.

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, (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) * A345762(k).