A345686 a(n) = n! * Sum_{k=1..n} n/floor(n/k)^2.

1, 5, 38, 222, 1974, 14640, 154580, 1476720, 17753400, 205430400, 2924030592, 38559628800, 623916216000, 9701871379200, 172359487872000, 3007238402488320, 60362232844193280, 1161408374590464000, 25603215951785472000, 547592177551491072000, 12990145748633044992000

Offset: 1

Author

Vaclav Kotesovec, Jun 23 2021

Keywords

• nonn

Links

• Mathoverflow, An asymptotic formula for a sum involving powers of floor functions, 2019.

Crossrefs

Cf. A345683.

Programs

Mathematica

Table[n! * Sum[n/Floor[n/k]^2, {k, 1, n}], {n, 1, 25}]
Table[n*n!*(Sum[(Floor[n/j] - Floor[n/(j + 1)])/j^2, {j, 1, n}]), {n, 1, 25}]

Formula

a(n) ~ c * n^2 * n!, where c = Sum_{j>-1} 1/(j^3*(j+1)) = zeta(3) - Pi^2/6 + 1.