A353891 Expansion of e.g.f. exp( (x * log(1-x))^2 / 4 ).

1, 0, 0, 0, 6, 30, 165, 1050, 8932, 86184, 909360, 10393020, 129313206, 1743627600, 25314159780, 393346535400, 6512022804960, 114430467296880, 2127154061337480, 41703621476302800, 859966710771029040, 18606040434320713920, 421427283751799685360

Offset: 0

Author

Seiichi Manyama, May 09 2022

Keywords

• nonn

Crossrefs

Cf. A066166, A353892, A353893.

Cf. A347001, A353880, A353894.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*log(1-x))^2/4)))

PARI

a(n) = n!*sum(k=0, n\4, (2*k)!*abs(stirling(n-2*k, 2*k, 1))/(4^k*k!*(n-2*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (2*k)! * |Stirling1(n-2*k,2*k)|/(4^k * k! * (n-2*k)!).