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 A365282 #12 Aug 31 2023 07:46:19
%S A365282 1,1,2,12,96,900,10800,157080,2634240,50455440,1089849600,26157479040,
%T A365282 690848040960,19924295751360,623024501299200,20996216063222400,
%U A365282 758724126031872000,29267547577396128000,1200407895406514995200
%N A365282 E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^2*A(x)).
%F A365282 a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(n-k+1,n-2*k)/( (n-k+1)*k! ).
%F A365282 a(n) ~ sqrt((s+1)/(2*s-1)) * (s-1)^((n+1)/2) * s^(n/2 + 1) * n^(n-1) / exp(n), where s = 3.011547791499065828694160466323712196300874261862... is the root of the equation (s-1)*LambertW(2*(s-1)^2/s) = 2. - _Vaclav Kotesovec_, Aug 31 2023
%t A365282 Join[{1}, Table[n! * Sum[(n-2*k)^k * Binomial[n-k+1,n-2*k] / ((n-k+1)*k!), {k,0,Floor[n/2]}], {n,1,20}]] (* _Vaclav Kotesovec_, Aug 31 2023 *)
%o A365282 (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(n-k+1, n-2*k)/((n-k+1)*k!));
%Y A365282 Cf. A358064, A365283, A365284.
%Y A365282 Cf. A365285.
%K A365282 nonn
%O A365282 0,3
%A A365282 _Seiichi Manyama_, Aug 31 2023