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

0,9

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = n! * Sum_{k=0..floor(n/8)} (4*k)! * |Stirling1(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*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)!));

Crossrefs

Cf. A066166, A353891, A353892.

Cf. A347003, A353882, A353896.

Sequence in context: A361610 A353896 A353885 * A353882 A061606 A331351

Adjacent sequences: A353890 A353891 A353892 * A353894 A353895 A353896

Keyword

nonn

Author

Seiichi Manyama, May 09 2022

Status

approved