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 A249459 #16 Dec 04 2021 05:56:06 %S A249459 1,1,17,794,72354,10874275,2438235715,762963987380,317685943157892, %T A249459 169842891165484965,113394131858832552133,92465351109879998121806, %U A249459 90431265068257318469676710,104479466717230437574945525959,140782828210237288756752539959687 %N A249459 a(n) = Sum_{k=0..n} k^(2*n). %H A249459 Seiichi Manyama, <a href="/A249459/b249459.txt">Table of n, a(n) for n = 0..214</a> %F A249459 E.g.f.: Sum_{n>=0} exp(n^2*x). %F A249459 a(n) ~ exp(2)/(exp(2)-1) * n^(2*n). %F A249459 G.f.: Sum_{k>=0} (k^2 * x)^k/(1 - k^2 * x). - _Seiichi Manyama_, Dec 03 2021 %t A249459 Table[Sum[k^(2*n),{k,1,n}],{n,1,20}] %t A249459 Table[n!*SeriesCoefficient[Sum[Exp[k^2*x], {k, 1, n}],{x,0,n}], {n,1,20}] %o A249459 (PARI) a(n)=n!*polcoeff(sum(k=0, n, exp(k*x+x*O(x^n))^k), n); %o A249459 for(n=1, 20, print1(a(n), ", ")) %o A249459 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^k/(1-k^2*x))) \\ _Seiichi Manyama_, Dec 03 2021 %Y A249459 Cf. A031971, A224899, A249489. %K A249459 nonn %O A249459 0,3 %A A249459 _Vaclav Kotesovec_, Oct 29 2014 %E A249459 a(0)=1 prepended by _Seiichi Manyama_, Dec 03 2021