A380675 - OEIS

%I #9 Jan 30 2025 11:23:35

%S 1,3,27,436,10377,329016,13079971,626414496,35132554449,2259697340800,

%T 164013549475371,13263204195136512,1182645846100592473,

%U 115285805003164594176,12197859187688440506675,1392237638583170475298816,170517388925776876433310369,22307473046095249063001554944

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

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

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

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

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

%Y Cf. A377832, A380665, A380666, A380674.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 30 2025