A377829 - OEIS

%I #11 Nov 09 2024 08:01:09

%S 1,3,25,364,7713,216216,7568041,318256800,15644919681,880848974080,

%T 55912403743161,3951344780946432,307737594185310625,

%U 26190457718737019904,2418475248758250599625,240846113359411822759936,25731326615411044591298049,2935802801104074173428531200

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

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

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

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

%F a(n) ~ (2*(1 + sqrt(2)))^(n + 1/2) * n^(n-1) / exp((2 - sqrt(2))*n + 1 - sqrt(2)). - _Vaclav Kotesovec_, Nov 09 2024

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

%Y Cf. A088690, A377830.

%Y Cf. A377827.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 09 2024