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%I #15 Nov 19 2023 10:41:19
%S 1,1,15,666,59230,8775075,1948891581,605698755508,250914820143996,
%T 133610836793706405,88919025666286620475,72317513878698256697166,
%U 70571883548815735717843290,81383769918571603591381635271
%N a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(2*n).
%F G.f.: Sum_{k>=0} (k^2 * x)^k/(1 + k^2 * x).
%F a(n) ~ 1/(1 + exp(-2)) * n^(2*n). - _Vaclav Kotesovec_, Dec 10 2021
%t Join[{1},Table[Sum[(-1)^(n-k) k^(2n),{k,0,n}],{n,20}]] (* _Harvey P. Dale_, Nov 19 2023 *)
%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*k^(2*n));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^k/(1+k^2*x)))
%Y Cf. A120485, A249459, A349884, A349891, A349902.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Dec 04 2021
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