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A352983
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a(n) = Sum_{k=0..floor(n/2)} k^(2*n).
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5
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1, 0, 1, 1, 257, 1025, 535538, 4799354, 4338079554, 69107159370, 96470431101379, 2401809362313955, 4798267740520031875, 172076350440523281571, 466164803742660494432996, 22761346686115003736962100, 80340572151131167125889902852
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} (k^2 * x)^(2 * k) / (1 - k^2 * x).
a(n) ~ exp(3 + (-1)^n) * (n/2)^(2*n) / (exp(4) - 1). - Vaclav Kotesovec, Apr 14 2022
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MATHEMATICA
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a[0] = 1; a[n_] := Sum[k^(2*n), {k, 0, Floor[n/2]}]; Array[a, 17, 0] (* Amiram Eldar, Apr 13 2022 *)
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PROG
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(PARI) a(n) = sum(k=0, n\2, k^(2*n));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^(2*k)/(1-k^2*x)))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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