A353893 - OEIS

%I #10 May 10 2022 11:40:31

%S 1,0,0,0,0,0,0,0,70,1260,17850,242550,3350655,48108060,724403680,

%T 11478967500,191601229820,3367499575440,62253354650760,

%U 1208755315895400,24611454394536780,524613603866302440,11687734234226039220,271715852337632107020

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

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

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

%o (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)!));

%Y Cf. A066166, A353891, A353892.

%Y Cf. A347003, A353882, A353896.

%K nonn

%O 0,9

%A _Seiichi Manyama_, May 09 2022