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 A364980 #11 Nov 18 2023 04:37:41
%S A364980 1,1,4,33,412,6945,147846,3807601,115151464,4001162913,157096369450,
%T A364980 6878742553881,332361857826780,17566215943990753,1008161606338206334,
%U A364980 62440146891413434305,4151012174991960338896,294834882756167048975553
%N A364980 E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x*A(x)^2).
%F A364980 a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(2*n-k+1,k)/( (2*n-k+1)*(n-k)! ).
%F A364980 a(n) ~ sqrt((1 + r*s^2)/(6 + 4*r*s^2)) * n^(n-1) / (exp(n) * r^(n + 1/2)), where r = 0.2190923703746024362724546703711998154573791458000... and s = 1.747404632046819382844696016554403302840973484745... are real roots of the system of equations 1 + exp(r*s^2)*r*s = s, 2*r*s^2*(s-1) = 1. - _Vaclav Kotesovec_, Nov 18 2023
%t A364980 Join[{1}, Table[n! * Sum[k^(n-k) * Binomial[2*n-k+1,k] / ((2*n-k+1)*(n-k)!), {k,0,n}], {n,1,20}]] (* _Vaclav Kotesovec_, Nov 18 2023 *)
%o A364980 (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(2*n-k+1, k)/((2*n-k+1)*(n-k)!));
%Y A364980 Cf. A006153, A161633, A161635, A364981.
%K A364980 nonn
%O A364980 0,3
%A A364980 _Seiichi Manyama_, Aug 15 2023