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

Author

Seiichi Manyama, May 09 2022

Keywords

• nonn

Crossrefs

Cf. A052506, A353894, A353895.

Cf. A327505, A353885, A353893.

Programs

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)!));

Formula

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