A356298 a(n) = n! * Sum_{k=1..n} sigma_2(k)/k.
1, 7, 41, 290, 2074, 18444, 165108, 1749264, 19412496, 241299360, 3097006560, 45546606720, 673536159360, 10986261431040, 187460277177600, 3445281394329600, 64637392771123200, 1325310849663897600, 27498565425087590400, 616389533324974080000
Offset: 1
Keywords
Programs
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Mathematica
Table[n! * Sum[DivisorSigma[2, k]/k, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 07 2022 *) -
PARI
a(n) = n!*sum(k=1, n, sigma(k, 2)/k);
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k*(1-x^k)^2))/(1-x))) -
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, k*log(1-x^k))/(1-x)))
Formula
E.g.f.: (1/(1-x)) * Sum_{k>0} x^k/(k * (1 - x^k)^2).
E.g.f.: -(1/(1-x)) * Sum_{k>0} k * log(1 - x^k).
a(n) ~ n! * zeta(3) * n^2 / 2. - Vaclav Kotesovec, Aug 07 2022