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 A371836 #11 Apr 08 2024 04:51:13
%S A371836 1,1,5,19,91,426,2190,11467,63811,365806,2200978,13677962,88553726,
%T A371836 591576220,4093814812,29164567635,214244414371,1616044475734,
%U A371836 12523774634922,99418836782602,808492937082410,6720935024074092,57100849909374340,495022008799053006
%N A371836 a(n) = Sum_{k=0..floor(n/2)} n^k * binomial(2*n-2*k-1,n-2*k).
%F A371836 a(n) = [x^n] 1/((1-n*x^2) * (1-x)^n).
%F A371836 a(n) ~ exp(sqrt(n) + 1/2) * n^(n/2) / 2. - _Vaclav Kotesovec_, Apr 08 2024
%t A371836 Join[{1}, Table[Sum[n^k*Binomial[2*n-2*k-1,n-1], {k, 0, n/2}], {n, 1, 25}]] (* _Vaclav Kotesovec_, Apr 08 2024 *)
%o A371836 (PARI) a(n) = sum(k=0, n\2, n^k*binomial(2*n-2*k-1, n-2*k));
%Y A371836 Cf. A293574, A371837.
%Y A371836 Cf. A371798, A371826.
%K A371836 nonn
%O A371836 0,3
%A A371836 _Seiichi Manyama_, Apr 08 2024