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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.

A356339 a(n) = Sum_{k=1..n} binomial(2*n, n-k) * sigma_2(k).

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%I A356339 #7 Aug 05 2022 06:09:08
%S A356339 1,9,55,297,1496,7215,33783,154825,698077,3107424,13690161,59802471,
%T A356339 259377080,1118176887,4795381640,20472223529,87051685546,368857919085,
%U A356339 1558036408998,6562564601592,27571934249754,115574440020477,483444570596465,2018365519396135,8411811012694246
%N A356339 a(n) = Sum_{k=1..n} binomial(2*n, n-k) * sigma_2(k).
%F A356339 a(n) ~ zeta(3) * n * 4^(n-1).
%t A356339 Table[Sum[Binomial[2*n, n-k]*DivisorSigma[2, k], {k, 1, n}], {n, 1, 30}]
%o A356339 (PARI) a(n) = sum(k=1, n, binomial(2*n, n-k) * sigma(k, 2)); \\ _Michel Marcus_, Aug 05 2022
%Y A356339 Cf. A001157, A064602, A351146, A356038.
%K A356339 nonn
%O A356339 1,2
%A A356339 _Vaclav Kotesovec_, Aug 04 2022