A379660 Expansion of e.g.f. (1/x) * Series_Reversion( x * (exp(-x) - 3*x) ).

1, 4, 63, 1861, 82097, 4850511, 360275791, 32284172215, 3391036374849, 408722465393947, 55615320933323831, 8433939560030789091, 1410592999486776429841, 257966146919938099737511, 51211682886276933924579999, 10968423456294584033965364191, 2521058533839507726700577317889

Offset: 0

Author

Seiichi Manyama, Dec 29 2024

Keywords

• nonn

Crossrefs

Cf. A000272, A377890, A379659.

Programs

PARI

a(n) = n!*sum(k=0, n, 3^(n-k)*(2*n-k+1)^(k-1)*binomial(2*n-k+1, n-k)/k!);

Formula

a(n) = n! * Sum_{k=0..n} 3^(n-k) * (2*n-k+1)^(k-1) * binomial(2*n-k+1,n-k)/k!.