A345682 a(n) = n! * Sum_{k=1..n} 1/(k*floor(n/k)).

1, 2, 7, 26, 148, 804, 6228, 47424, 441936, 4288320, 50437440, 560373120, 7723935360, 106618256640, 1614841401600, 25127582054400, 446784010444800, 7727747269939200, 152873884406476800, 2966599550251008000, 62987912790921216000, 1378192085174919168000

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..449

Vaclav Kotesovec, Plot of a(n)/n! for n = 1..1000000

Formula

a(n) ~ c * n!, where c = Sum_{j>=1} log(1 + 1/j)/j = A131688 = 1.25774...

E.g.f.: -(1/(1-x)) * Sum_{k>0} (1 - x^k) * log(1 - x^k)/k. - Seiichi Manyama, Jul 23 2022

Mathematica

Table[n! * Sum[1/(k*Floor[n/k]), {k, 1, n}], {n, 1, 25}]
Table[n! * Sum[(HarmonicNumber[Floor[n/j]] - HarmonicNumber[Floor[n/(1 + j)]])/j, {j, 1, n}], {n, 1, 25}]

Prog

(PARI) a(n) = n!*sum(k=1, n, 1/(k*(n\k))); \\ Michel Marcus, Jun 24 2021
(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

Crossrefs

Cf. A006218, A010786, A024917, A092143, A117871, A345683, A345684.

Sequence in context: A209005 A361242 A068870 * A005519 A290305 A343595

Adjacent sequences: A345679 A345680 A345681 * A345683 A345684 A345685

Keyword

nonn

Author

Vaclav Kotesovec, Jun 23 2021

Status

approved