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 A377526 #12 Nov 11 2024 13:28:15
%S A377526 1,1,12,273,9604,460105,27966126,2062219117,178897527768,
%T A377526 17853102321489,2014988044093210,253792946798597701,
%U A377526 35290880970687039732,5370055269772474994713,887591963820839894529654,158357028389450319651183165,30332317748593431632078480176,6208425034878692992471996557217
%N A377526 E.g.f. satisfies A(x) = 1 + x*exp(x)*A(x)^5.
%C A377526 In general, for k > 1, if e.g.f. satisfies A(x) = 1 + x*exp(x)*A(x)^k, then a(n) ~ sqrt(k*(1 + LambertW((k-1)^(k-1)/k^k))) * n^(n-1) / ((k-1)^(3/2) * exp(n) * LambertW((k-1)^(k-1)/k^k)^n). - _Vaclav Kotesovec_, Nov 11 2024
%F A377526 a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(5*k,k)/( (4*k+1)*(n-k)! ) = n! * Sum_{k=0..n} k^(n-k) * A002294(k)/(n-k)!.
%F A377526 a(n) ~ sqrt(5*(1 + LambertW(256/3125))) * n^(n-1) / (8 * exp(n) * LambertW(256/3125)^n). - _Vaclav Kotesovec_, Nov 11 2024
%o A377526 (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(5*k, k)/((4*k+1)*(n-k)!));
%Y A377526 Cf. A006153, A295238, A364983, A364987.
%Y A377526 Cf. A002294.
%K A377526 nonn
%O A377526 0,3
%A A377526 _Seiichi Manyama_, Oct 30 2024