OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..448
FORMULA
a(n) ~ c * n^2 * n!, where c = Sum_{j>=1} (2*j + 1) / (2*j^3*(j+1)^2) = Pi^2/12 + zeta(3)/2 - 1 = 0.423495...
E.g.f.: -(1/(1-x)) * Sum_{k>0} k * (1 - x^k) * log(1 - x^k). - Seiichi Manyama, Jul 23 2022
MATHEMATICA
Table[n!*Sum[k/Floor[n/k], {k, 1, n}], {n, 1, 25}]
Table[n!*Sum[(Floor[n/j] - Floor[n/(1 + j)])*((1 + Floor[n/j] + Floor[n/(1 + j)])/2/j), {j, 1, n}], {n, 1, 25}]
PROG
(PARI) a(n) = n!*sum(k=1, n, k/(n\k)); \\ Michel Marcus, Jun 23 2021
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, k*(1-x^k)*log(1-x^k))/(1-x))) \\ Seiichi Manyama, Jul 23 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 23 2021
STATUS
approved