A353893 Expansion of e.g.f. exp( (x * log(1-x))^4 / 576 ).

1, 0, 0, 0, 0, 0, 0, 0, 70, 1260, 17850, 242550, 3350655, 48108060, 724403680, 11478967500, 191601229820, 3367499575440, 62253354650760, 1208755315895400, 24611454394536780, 524613603866302440, 11687734234226039220, 271715852337632107020

Offset: 0

Author

Seiichi Manyama, May 09 2022

Keywords

• nonn

Crossrefs

Cf. A066166, A353891, A353892.

Cf. A347003, A353882, A353896.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*log(1-x))^4/576)))

PARI

a(n) = n!*sum(k=0, n\8, (4*k)!*abs(stirling(n-4*k, 4*k, 1))/(576^k*k!*(n-4*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/8)} (4*k)! * |Stirling1(n-4*k,4*k)|/(576^k * k! * (n-4*k)!).