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%I #16 Aug 07 2022 04:57:27
%S 1,5,23,134,814,6324,50028,475824,4806576,54597600,644119200,
%T 8847100800,121718332800,1853505158400,29894856364800,518855607244800,
%U 9197155541145600,179420609436364800,3537039053405491200,75849875285280768000,1670700245252548608000
%N a(n) = n! * Sum_{k=1..n} floor(n/k)/k.
%F E.g.f.: (1/(1-x)) * Sum_{k>0} x^k/(k * (1 - x^k)).
%F E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1 - x^k).
%F a(n) ~ c * n! * n, where c = Pi^2/6. - _Vaclav Kotesovec_, Aug 02 2022
%F a(n) = n! * Sum_{k=1..n} sigma(k)/k. - _Seiichi Manyama_, Aug 03 2022
%o (PARI) a(n) = n!*sum(k=1, n, n\k/k);
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k*(1-x^k)))/(1-x)))
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k))/(1-x)))
%o (PARI) a(n) = n!*sum(k=1, n, sigma(k)/k); \\ _Seiichi Manyama_, Aug 03 2022
%Y Cf. A038048, A355886.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jul 23 2022