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 A377574 #10 Nov 02 2024 07:41:49
%S A377574 1,2,14,150,2264,44370,1073772,30998954,1041094448,39909978594,
%T A377574 1720526113460,82422717484602,4345035540566184,250012958308399442,
%U A377574 15594180423126432428,1048169467357831893930,75535629221800163853152,5810132660615400890909634,475146028302302130377698404
%N A377574 E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x))^2.
%F A377574 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A295238.
%F A377574 a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(2*k+2,k)/( (k+1)*(n-k)! ).
%F A377574 a(n) ~ 2^(5/2) * sqrt(1 + LambertW(1/4)) * n^(n-1) / (LambertW(1/4)^n * exp(n)). - _Vaclav Kotesovec_, Nov 02 2024
%o A377574 (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(2*k+2, k)/((k+1)*(n-k)!));
%Y A377574 Cf. A006153, A377575, A377576.
%Y A377574 Cf. A002999, A295238, A377553.
%K A377574 nonn
%O A377574 0,2
%A A377574 _Seiichi Manyama_, Nov 02 2024