A356338 a(n) = Sum_{k=1..n} binomial(2*n, n-k) * sigma(k).

1, 7, 37, 179, 826, 3703, 16283, 70619, 303121, 1290682, 5460511, 22981019, 96296552, 402024497, 1673116072, 6944105579, 28752345362, 118801061059, 489959398840, 2017339105514, 8293732341134, 34051489445365, 139634028015269, 571955737066307, 2340402722605976, 9567794393004816

Offset: 1

Author

Vaclav Kotesovec, Aug 04 2022

Keywords

• nonn

Crossrefs

Cf. A000203, A024916, A185003, A351146.

Programs

Mathematica

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

PARI

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

Formula

a(n) ~ Pi^(3/2) * 4^(n-1) * sqrt(n) / 3.