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 A372160 #17 Aug 27 2025 03:35:06
%S A372160 1,2,8,56,568,7592,126364,2522060,58760272,1566368432,47036927284,
%T A372160 1571615915828,57841636573912,2325362549256008,101399801919677356,
%U A372160 4767244262108645948,240395075369097851296,12943276401835227578720,741127491503124866498404
%N A372160 E.g.f. A(x) satisfies A(x) = exp( 2 * x / (1 - x * A(x)^(1/2)) ).
%F A372160 E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A161630.
%F A372160 If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(n+(s-1)*k-1,n-k)/k!.
%F A372160 a(n) ~ (1 + 2*LambertW(1/2))^(n + 1/2) * n^(n-1) / (sqrt(1 + LambertW(1/2)) * 2^(2*n+3) * exp(n) * LambertW(1/2)^(2*n + 7/2)). - _Vaclav Kotesovec_, Aug 27 2025
%t A372160 terms=19; A[_]=1; Do[A[x_] = Exp[2*x/(1-x*Sqrt[A[x]])] + O[x]^terms // Normal, terms];CoefficientList[Series[A[x],{x,0,terms}],x]Range[0,terms-1]! (* _Stefano Spezia_, Aug 26 2025 *)
%o A372160 (PARI) a(n, r=2, s=1, t=0, u=1) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(n+(s-1)*k-1, n-k)/k!);
%Y A372160 Cf. A161630.
%K A372160 nonn,changed
%O A372160 0,2
%A A372160 _Seiichi Manyama_, Apr 20 2024