A369756 Expansion of e.g.f. exp( (1 - (1+x)^5)/5 ).

1, -1, -3, -1, 49, 255, -275, -13105, -83775, 170495, 8290045, 69257055, -111005135, -9684015745, -109196883795, -31470300625, 17728458119425, 276531029694975, 904537471692925, -44728487203650625, -1000823562359108175, -7110596979389965825

Offset

0,3

Links

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

Eric Weisstein's World of Mathematics, Bell Polynomial.

Formula

a(0) = 1; a(n) = -(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) * Bell_k(-1/5), where Bell_n(x) is n-th Bell polynomial.

Prog

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

Crossrefs

Cf. A001464, A252284, A369755.

Cf. A049427, A369753.

Sequence in context: A354391 A223173 A010292 * A133104 A322730 A292425

Adjacent sequences: A369753 A369754 A369755 * A369757 A369758 A369759

Keyword

sign

Author

Seiichi Manyama, Jan 31 2024

Status

approved