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.
%I A356345 #7 Aug 05 2022 06:15:34 %S A356345 2,32,232,1702,8254,54454,226054,1320004,5744424,29762704,115825408, %T A356345 683698168,2451800168,12480950168,52811505368,257779918358, %U A356345 934525722158,5063712283658,17858697779258,93122902514978,362251839734978,1645752207604178,6009470493232178,33419933623867178 %N A356345 a(n) = Sum_{k=1..n} binomial(2*k, k) * sigma_2(k). %C A356345 The average value of a(n) is zeta(3) * n^(3/2) * 4^(n+1) / (3*sqrt(Pi)). %t A356345 Table[Sum[Binomial[2*k, k]*DivisorSigma[2, k], {k, 1, n}], {n, 1, 30}] %o A356345 (PARI) a(n) = sum(k=1, n, binomial(2*k, k) * sigma(k, 2)); \\ _Michel Marcus_, Aug 05 2022 %Y A356345 Cf. A001157, A064602, A351146, A356038. %K A356345 nonn %O A356345 1,1 %A A356345 _Vaclav Kotesovec_, Aug 04 2022