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

1, 9, 55, 297, 1496, 7215, 33783, 154825, 698077, 3107424, 13690161, 59802471, 259377080, 1118176887, 4795381640, 20472223529, 87051685546, 368857919085, 1558036408998, 6562564601592, 27571934249754, 115574440020477, 483444570596465, 2018365519396135, 8411811012694246

Offset: 1

Author

Vaclav Kotesovec, Aug 04 2022

Keywords

• nonn

Crossrefs

Cf. A001157, A064602, A351146, A356038.

Programs

Mathematica

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

PARI

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

Formula

a(n) ~ zeta(3) * n * 4^(n-1).