A335811 E.g.f.: exp(x) * Product_{k>=1} (1 + (1 - exp(x))^k).

1, 0, 0, -6, -36, -270, -1620, -8526, -41076, -549870, -13520340, -262959246, -3587233716, -22581847470, 584571618540, 30096769542834, 859315925548044, 18434866643574930, 285138881159407020, 2045091797042889714, -28367019385288799796, 379914681728984325330

Offset

0,4

Comments

Stirling-Bernoulli transform of A000009.

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..n} (-1)^k * Stirling2(n+1,k+1) * k! * A000009(k).

Mathematica

nmax = 21; CoefficientList[Series[Exp[x] Product[(1 + (1 - Exp[x])^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^k StirlingS2[n + 1, k + 1] k! PartitionsQ[k], {k, 0, n}], {n, 0, 21}]

Crossrefs

Cf. A000009, A305550, A327601.

Sequence in context: A221461 A090015 A299330 * A144892 A204210 A366436

Adjacent sequences: A335808 A335809 A335810 * A335812 A335813 A335814

Keyword

sign

Author

Ilya Gutkovskiy, Jun 25 2020

Status

approved