This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A377831 #13 Apr 02 2025 07:20:42
%S A377831 1,2,13,154,2701,63216,1856569,65711024,2724349401,129552751360,
%T A377831 6952877604421,415770771875328,27416031835737637,1976460653044957184,
%U A377831 154658036515292528625,13055394531339601033216,1182611605875201470044081,114426900236922150187892736
%N A377831 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-x) ).
%H A377831 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A377831 E.g.f. A(x) satisfies A(x) = exp(x * A(x))/(1 - x*A(x)).
%F A377831 a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n-k,n-k)/k!.
%F A377831 a(n) ~ phi^(3*n + 3/2) * n^(n-1) / (5^(1/4) * exp((n+1)/phi - 1)), where phi = A001622 = (1 + sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Nov 09 2024
%o A377831 (PARI) a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(2*n-k, n-k)/k!);
%Y A377831 Cf. A001622, A377832, A377833.
%K A377831 nonn
%O A377831 0,2
%A A377831 _Seiichi Manyama_, Nov 09 2024