A353665 Expansion of e.g.f. exp((exp(x) - 1)^4).

1, 0, 0, 0, 24, 240, 1560, 8400, 60984, 912240, 15938520, 242998800, 3300493944, 44583979440, 690641504280, 12868117189200, 264164524958904, 5481631005177840, 112822632387018840, 2367468210865875600, 52624238539033647864, 1258531092544541563440

Offset

0,5

Links

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

Formula

E.g.f.: exp((exp(x) - 1)^4).

G.f.: Sum_{k>=0} (4*k)! * x^(4*k)/(k! * Product_{j=1..4*k} (1 - j * x)).

a(0) = 1; a(n) = 24 * Sum_{k=1..n} binomial(n-1,k-1) * Stirling2(k,4) * a(n-k).

a(n) = Sum_{k=0..floor(n/4)} (4*k)! * Stirling2(n,4*k)/k!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((exp(x)-1)^4)))
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (4*k)!*x^(4*k)/(k!*prod(j=1, 4*k, 1-j*x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=24*sum(j=1, i, binomial(i-1, j-1)*stirling(j, 4, 2)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\4, (4*k)!*stirling(n, 4*k, 2)/k!);

Crossrefs

Cf. A000110, A052859, A353664.

Cf. A327505, A353358, A353775.

Sequence in context: A052796 A056269 A000919 * A353775 A268966 A014340

Adjacent sequences: A353662 A353663 A353664 * A353666 A353667 A353668

Keyword

nonn

Author

Seiichi Manyama, May 07 2022

Status

approved