A353885 Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^4 / 576).

1, 0, 0, 0, 0, 0, 0, 0, 70, 1260, 13650, 115500, 841995, 5555550, 34139105, 198948750, 1175994820, 10315705400, 192609389700, 4563951046200, 98992258506345, 1898260633492650, 32787422848455275, 520556451785466250, 7722233521138092726, 108688302800107222500

Offset: 0

Author

Seiichi Manyama, May 09 2022

Keywords

• nonn

Crossrefs

Cf. A052848, A353883, A353884.

Cf. A346895, A353882.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(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*(n-4*k)!));

Formula

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