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
Keywords
Programs
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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.