A369753 Expansion of e.g.f. exp(1 - (1+x)^5).

1, -5, 5, 115, -95, -8245, -21275, 896275, 8801825, -95466725, -2703832475, -3522650125, 717727962625, 9961465952875, -118944021914875, -5634631318806125, -37511809003469375, 2020875725751906875, 55489065505990733125, -65182838564153418125

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(0) = 1; a(n) = -5 * (n-1)! * Sum_{k=1..min(5,n)} binomial(4,k-1) * a(n-k)/(n-k)!.

a(n) = Sum_{k=0..n} 5^k * Stirling1(n,k) * A000587(k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-(1+x)^5)))

Crossrefs

Column k=5 of A369738.

Cf. A000587, A202825.

Sequence in context: A081049 A048607 A229767 * A215729 A364452 A094463

Adjacent sequences: A369750 A369751 A369752 * A369754 A369755 A369756

Keyword

sign

Author

Seiichi Manyama, Jan 30 2024

Status

approved