A356344 a(n) = Sum_{k=1..n} binomial(2*k, k) * sigma(k).

2, 20, 100, 590, 2102, 13190, 40646, 233696, 865756, 4191364, 12656548, 88372916, 233981316, 1196779716, 4919600196, 23553092286, 65558004246, 419488280946, 1126393556946, 6915947767386, 24140199749466, 99887762443386, 297490099905786, 2232346320891786, 6151075120462098

Offset: 1

Author

Vaclav Kotesovec, Aug 04 2022

Keywords

• nonn

Comments

The average value of a(n) is Pi^(3/2) * sqrt(n) * 2^(2*n+1) / 9.

Crossrefs

Cf. A000203, A024916, A185003, A351146.

Programs

Mathematica

Table[Sum[Binomial[2*k, k]*DivisorSigma[1, k], {k, 1, n}], {n, 1, 30}]

PARI

a(n) = sum(k=1, n, binomial(2*k, k) * sigma(k)); \\ Michel Marcus, Aug 05 2022