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%I #16 Dec 04 2021 05:56:06
%S 1,1,17,794,72354,10874275,2438235715,762963987380,317685943157892,
%T 169842891165484965,113394131858832552133,92465351109879998121806,
%U 90431265068257318469676710,104479466717230437574945525959,140782828210237288756752539959687
%N a(n) = Sum_{k=0..n} k^(2*n).
%H Seiichi Manyama, <a href="/A249459/b249459.txt">Table of n, a(n) for n = 0..214</a>
%F E.g.f.: Sum_{n>=0} exp(n^2*x).
%F a(n) ~ exp(2)/(exp(2)-1) * n^(2*n).
%F G.f.: Sum_{k>=0} (k^2 * x)^k/(1 - k^2 * x). - _Seiichi Manyama_, Dec 03 2021
%t Table[Sum[k^(2*n),{k,1,n}],{n,1,20}]
%t Table[n!*SeriesCoefficient[Sum[Exp[k^2*x], {k, 1, n}],{x,0,n}], {n,1,20}]
%o (PARI) a(n)=n!*polcoeff(sum(k=0, n, exp(k*x+x*O(x^n))^k), n);
%o for(n=1, 20, print1(a(n), ", "))
%o (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 Cf. A031971, A224899, A249489.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 29 2014
%E a(0)=1 prepended by _Seiichi Manyama_, Dec 03 2021
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