A380675 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x * (1 - x)) ).

1, 3, 27, 436, 10377, 329016, 13079971, 626414496, 35132554449, 2259697340800, 164013549475371, 13263204195136512, 1182645846100592473, 115285805003164594176, 12197859187688440506675, 1392237638583170475298816, 170517388925776876433310369, 22307473046095249063001554944

Offset: 0

Author

Seiichi Manyama, Jan 30 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A377832, A380665, A380666, A380674.

Programs

PARI

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

Formula

E.g.f. A(x) satisfies A(x) = exp(x * A(x) * (1 - x*A(x)))/(1 - x*A(x))^2.

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