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 A377859 #10 Nov 10 2024 03:34:55
%S A377859 1,0,1,2,21,144,1765,21552,340137,5845760,116495721,2550320640,
%T A377859 62023290109,1642735460352,47321500546125,1469008742856704,
%U A377859 48962556079079505,1742660440701861888,65993849612007279697,2648999558505185280000,112360563741545020804581
%N A377859 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(x) ).
%H A377859 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A377859 E.g.f. A(x) satisfies A(x) = exp(-x * A(x))/(1 - x*A(x)).
%F A377859 a(n) = n! * Sum_{k=0..n} (-1)^k * (n+1)^(k-1) * binomial(2*n-k,n-k)/k!.
%F A377859 a(n) ~ phi^(3*n + 3/2) * n^(n-1) / (5^(1/4) * exp(phi*n + 1/phi)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Nov 10 2024
%o A377859 (PARI) a(n) = n!*sum(k=0, n, (-1)^k*(n+1)^(k-1)*binomial(2*n-k, n-k)/k!);
%Y A377859 Cf. A377860, A377861.
%Y A377859 Cf. A377831.
%K A377859 nonn
%O A377859 0,4
%A A377859 _Seiichi Manyama_, Nov 09 2024