A356345 a(n) = Sum_{k=1..n} binomial(2*k, k) * sigma_2(k).

2, 32, 232, 1702, 8254, 54454, 226054, 1320004, 5744424, 29762704, 115825408, 683698168, 2451800168, 12480950168, 52811505368, 257779918358, 934525722158, 5063712283658, 17858697779258, 93122902514978, 362251839734978, 1645752207604178, 6009470493232178, 33419933623867178

Offset: 1

Author

Vaclav Kotesovec, Aug 04 2022

Keywords

• nonn

Comments

The average value of a(n) is zeta(3) * n^(3/2) * 4^(n+1) / (3*sqrt(Pi)).

Crossrefs

Cf. A001157, A064602, A351146, A356038.

Programs

Mathematica

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

PARI

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