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%I #28 Jul 23 2022 09:53:45
%S 1,2,7,26,148,804,6228,47424,441936,4288320,50437440,560373120,
%T 7723935360,106618256640,1614841401600,25127582054400,446784010444800,
%U 7727747269939200,152873884406476800,2966599550251008000,62987912790921216000,1378192085174919168000
%N a(n) = n! * Sum_{k=1..n} 1/(k*floor(n/k)).
%H Seiichi Manyama, <a href="/A345682/b345682.txt">Table of n, a(n) for n = 1..449</a>
%H Vaclav Kotesovec, <a href="/A345682/a345682.jpg">Plot of a(n)/n! for n = 1..1000000</a>
%F a(n) ~ c * n!, where c = Sum_{j>=1} log(1 + 1/j)/j = A131688 = 1.25774...
%F E.g.f.: -(1/(1-x)) * Sum_{k>0} (1 - x^k) * log(1 - x^k)/k. - _Seiichi Manyama_, Jul 23 2022
%t Table[n! * Sum[1/(k*Floor[n/k]), {k, 1, n}], {n, 1, 25}]
%t Table[n! * Sum[(HarmonicNumber[Floor[n/j]] - HarmonicNumber[Floor[n/(1 + j)]])/j, {j, 1, n}], {n, 1, 25}]
%o (PARI) a(n) = n!*sum(k=1, n, 1/(k*(n\k))); \\ _Michel Marcus_, Jun 24 2021
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, (1-x^k)*log(1-x^k)/k)/(1-x))) \\ _Seiichi Manyama_, Jul 23 2022
%Y Cf. A006218, A010786, A024917, A092143, A117871, A345683, A345684.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, Jun 23 2021
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