A356010 a(n) = n! * Sum_{k=1..n} floor(n/k)/k.

1, 5, 23, 134, 814, 6324, 50028, 475824, 4806576, 54597600, 644119200, 8847100800, 121718332800, 1853505158400, 29894856364800, 518855607244800, 9197155541145600, 179420609436364800, 3537039053405491200, 75849875285280768000, 1670700245252548608000

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

E.g.f.: (1/(1-x)) * Sum_{k>0} x^k/(k * (1 - x^k)).

E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1 - x^k).

a(n) ~ c * n! * n, where c = Pi^2/6. - Vaclav Kotesovec, Aug 02 2022

a(n) = n! * Sum_{k=1..n} sigma(k)/k. - Seiichi Manyama, Aug 03 2022

Prog

(PARI) a(n) = n!*sum(k=1, n, n\k/k);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k*(1-x^k)))/(1-x)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k))/(1-x)))
(PARI) a(n) = n!*sum(k=1, n, sigma(k)/k); \\ Seiichi Manyama, Aug 03 2022

Crossrefs

Cf. A038048, A355886.

Sequence in context: A239820 A077240 A281231 * A244786 A129098 A047049

Adjacent sequences: A356007 A356008 A356009 * A356011 A356012 A356013

Keyword

nonn

Author

Seiichi Manyama, Jul 23 2022

Status

approved