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A356436
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} d^(k/d) )/k.
3
1, 5, 23, 146, 874, 8124, 62628, 707664, 7860816, 103284000, 1179669600, 24454569600, 324615427200, 5740203974400, 119579523436800, 2688723275212800, 46084905896601600, 1383333631684300800, 26411386476116275200, 868104140064602112000
OFFSET
1,2
FORMULA
a(n) = n! * Sum_{k=1..n} A055225(k)/k.
E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1 - k*x^k)/k.
a(n) ~ (n-1)! * 3^((n + 3 - mod(n,3))/3)/2. - Vaclav Kotesovec, Aug 07 2022
PROG
(PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d))/k);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k)/k)/(1-x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 07 2022
STATUS
approved