A370986 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2/2*exp(x)) ).

1, 0, 1, 3, 24, 220, 2535, 35931, 588028, 11110212, 236355885, 5605425595, 146586048906, 4190560545678, 130037568893323, 4352949788266275, 156362710268877960, 5999465853656510056, 244887352806333261753, 10595948826118665719475, 484448170190529051468910

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A213644, A370987.

Cf. A346888, A370930.

Programs

PARI

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

PARI

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} k^(n-2*k) * (n+k)!/(2^k * k! * (n-2*k)!).