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A356600
a(n) = n! * Sum_{k=1..n} sigma_2(k)/(k * (n-k)!).
1
1, 7, 38, 240, 1509, 12115, 96326, 929432, 9421089, 108909943, 1249105054, 17862483320, 241674418101, 3676733397363, 59149265744302, 1058605924855568, 18041587282787489, 363409114370324295, 6970858463185187062, 153017341796727034336, 3360005220780469981157
OFFSET
1,2
COMMENTS
The average value of a(n) is zeta(3) * exp(1) * n * n!. - Vaclav Kotesovec, Aug 17 2022
FORMULA
E.g.f.: exp(x) * Sum_{k>0} x^k/(k * (1 - x^k)^2).
E.g.f.: -exp(x) * Sum_{k>0} k * log(1 - x^k).
MATHEMATICA
Table[n! * Sum[DivisorSigma[2, k]/(k * (n-k)!), {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 17 2022 *)
PROG
(PARI) a(n) = n!*sum(k=1, n, sigma(k, 2)/(k*(n-k)!));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=1, N, x^k/(k*(1-x^k)^2))))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, k*log(1-x^k))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 15 2022
STATUS
approved