A356372 a(n) = Sum_{k=1..n} binomial(2*n, k) * A000005(k).

2, 16, 76, 386, 1474, 7349, 26807, 121964, 487068, 2105087, 7486505, 37278746, 133488216, 550615531, 2263230587, 9856735046, 35168418266, 160420872009, 573578559659, 2582163925152, 10333237435638, 41122278086361, 146621866522577, 712999981650663, 2702556741014621

Offset: 1

Author

Vaclav Kotesovec, Aug 04 2022

Keywords

• nonn

Crossrefs

Cf. A000005, A006218, A160399, A351146.

Programs

Mathematica

Table[Sum[Binomial[2*n, k]*DivisorSigma[0, k], {k, 1, n}], {n, 1, 30}]

PARI

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

Formula

a(n) ~ 2^(2*n-1) * (log(n) + 2*gamma), where gamma is the Euler-Mascheroni constant A001620.