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 A360647 #10 Feb 16 2023 09:46:44 %S A360647 1,1,17,761,67739,10029956,2226004406,691381685259,286255287677425, %T A360647 152360721379689043,101358756787489940837,82408168580060017122144, %U A360647 80396790074312939684672316,92691781529853274368541343021 %N A360647 Expansion of Sum_{k>=0} (k^2 * x * (1 + x))^k. %F A360647 a(n) = Sum_{k=0..floor(n/2)} (n-k)^(2*(n-k)) * binomial(n-k,k). %F A360647 a(n) ~ n^(2*n). - _Vaclav Kotesovec_, Feb 16 2023 %t A360647 Flatten[{1, Table[Sum[Binomial[n-k,k] * (n-k)^(2*(n-k)), {k,0,n/2}], {n,1,30}]}] (* _Vaclav Kotesovec_, Feb 16 2023 *) %o A360647 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x*(1+x))^k)) %o A360647 (PARI) a(n) = sum(k=0, n\2, (n-k)^(2*(n-k))*binomial(n-k, k)); %Y A360647 Cf. A323280, A360611. %K A360647 nonn %O A360647 0,3 %A A360647 _Seiichi Manyama_, Feb 15 2023