A377832 - OEIS

%I #11 Nov 09 2024 08:19:35

%S 1,3,29,508,13137,452616,19549021,1016932512,61940154177,

%T 4325943203200,340900244374461,29927648769380352,2896829645184711121,

%U 306522175683831195648,35201889560564096132925,4360880891670519541927936,579686447990401730151243009,82304944815106131595482267648

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

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

%F a(n) ~ (1 + sqrt(3))^(4*n + 5/2) * n^(n-1) / (3^(1/4) * 2^(3*n + 5/2) * exp((sqrt(3) - 1)*n - 2 + sqrt(3))). - _Vaclav Kotesovec_, Nov 09 2024

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

%Y Cf. A377831, A377833.

%Y Cf. A377742, A377810.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 09 2024