A377832 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x) ).
1, 3, 29, 508, 13137, 452616, 19549021, 1016932512, 61940154177, 4325943203200, 340900244374461, 29927648769380352, 2896829645184711121, 306522175683831195648, 35201889560564096132925, 4360880891670519541927936, 579686447990401730151243009, 82304944815106131595482267648
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(3*n-k+1, n-k)/k!);
Formula
E.g.f. A(x) satisfies A(x) = exp(x * A(x))/(1 - x*A(x))^2.
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(3*n-k+1,n-k)/k!.
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