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%I #8 Jun 24 2021 13:40:13
%S 1,5,38,222,1974,14640,154580,1476720,17753400,205430400,2924030592,
%T 38559628800,623916216000,9701871379200,172359487872000,
%U 3007238402488320,60362232844193280,1161408374590464000,25603215951785472000,547592177551491072000,12990145748633044992000
%N a(n) = n! * Sum_{k=1..n} n/floor(n/k)^2.
%H Mathoverflow, <a href="https://mathoverflow.net/questions/338432/an-asymptotic-formula-for-a-sum-involving-powers-of-floor-functions">An asymptotic formula for a sum involving powers of floor functions</a>, 2019.
%F a(n) ~ c * n^2 * n!, where c = Sum_{j>-1} 1/(j^3*(j+1)) = zeta(3) - Pi^2/6 + 1.
%t Table[n! * Sum[n/Floor[n/k]^2, {k, 1, n}], {n, 1, 25}]
%t Table[n*n!*(Sum[(Floor[n/j] - Floor[n/(j + 1)])/j^2, {j, 1, n}]), {n, 1, 25}]
%Y Cf. A345683.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, Jun 23 2021