A354398 Expansion of e.g.f. exp( -(exp(x) - 1)^5 / 120 ).

1, 0, 0, 0, 0, -1, -15, -140, -1050, -6951, -42399, -239800, -1164570, -2553551, 54771717, 1384600854, 23301803070, 340911045929, 4600861076433, 58236569430172, 687816515641206, 7315220762286129, 61629305427537309, 140107851269900954, -11001310744922517426

Offset

0,7

Links

Table of n, a(n) for n=0..24.

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n-1,k-1) * Stirling2(k,5) * a(n-k).

a(n) = Sum_{k=0..floor(n/5)} (5*k)! * Stirling2(n,5*k)/((-120)^k * k!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-(exp(x)-1)^5/120)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, binomial(i-1, j-1)*stirling(j, 5, 2)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 2)/((-120)^k*k!));

Crossrefs

Cf. A000587, A354395, A354396, A354397.

Cf. A327506, A346977, A354394.

Sequence in context: A002803 A354394 A346977 * A056281 A000481 A365528

Adjacent sequences: A354395 A354396 A354397 * A354399 A354400 A354401

Keyword

sign

Author

Seiichi Manyama, May 25 2022

Status

approved