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%I #7 Aug 05 2022 06:12:05
%S 2,34,281,2178,12397,79729,398932,2224354,10959221,56341309,255685080,
%T 1334248401,5892916876,28082515768,127714609741,604178948098,
%U 2590365128017,12284868071365,52160408294826,241445420212893,1049251819301974,4674022621994716,19563451165603647
%N a(n) = Sum_{k=1..n} binomial(2*n, k) * sigma_2(k).
%F a(n) ~ zeta(3) * n^2 * 2^(2*n-1).
%t Table[Sum[Binomial[2*n, k]*DivisorSigma[2, k], {k, 1, n}], {n, 1, 30}]
%o (PARI) a(n) = sum(k=1, n, binomial(2*n, k) * sigma(k, 2)); \\ _Michel Marcus_, Aug 05 2022
%Y Cf. A001157, A064602, A351146, A356038.
%K nonn
%O 1,1
%A _Vaclav Kotesovec_, Aug 04 2022