A377331 a(n) = Sum_{k=1..n} binomial(n,k) * sigma(k,n).
1, 7, 58, 707, 11186, 219202, 5097205, 137036819, 4179577045, 142539843882, 5374034016858, 221930535785918, 9962431381720780, 482997720973917947, 25151350530268841003, 1400042027334939211235, 82960609980815501293708, 5213812927633674297808237, 346394632975721545946690108
Offset: 1
Keywords
Programs
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Mathematica
Table[Sum[Binomial[n, k] * DivisorSigma[n, k], {k, 1, n}], {n, 1, 20}] -
PARI
{a(n)=sum(k=1, n, binomial(n, k)*sigma(k, n))}
Formula
a(n) ~ n^n / (sqrt(1 + LambertW(exp(-1))) * exp(n) * LambertW(exp(-1))^n).