A353896 Expansion of e.g.f. exp( (x * (exp(x) - 1))^4 / 576 ).

1, 0, 0, 0, 0, 0, 0, 0, 70, 1260, 13650, 115500, 841995, 5555550, 34139105, 198948750, 1144463320, 8171563400, 112204064700, 2364061354200, 49912312090845, 951208121086650, 16403948060775275, 260328078068154250, 3860274855288458376, 54182965918066177500

Offset

0,9

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = n! * Sum_{k=0..floor(n/8)} (4*k)! * Stirling2(n-4*k,4*k)/(576^k * k! * (n-4*k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(exp(x)-1))^4/576)))
(PARI) a(n) = n!*sum(k=0, n\8, (4*k)!*stirling(n-4*k, 4*k, 2)/(576^k*k!*(n-4*k)!));

Crossrefs

Cf. A052506, A353894, A353895.

Cf. A327505, A353885, A353893.

Sequence in context: A229735 A254472 A361610 * A353885 A353893 A353882

Adjacent sequences: A353893 A353894 A353895 * A353897 A353898 A353899

Keyword

nonn

Author

Seiichi Manyama, May 09 2022

Status

approved