A259409 The pi-based arithmetic derivative of the double factorial of n.
0, 0, 1, 2, 12, 19, 128, 193, 1600, 2997, 20224, 37692, 319488, 552366, 5164032, 10853055, 103268352, 198691110, 2199453696, 4050806490, 49934499840, 102089892240, 1176592711680, 2471811316695, 32489204613120, 71282307214125, 893769083781120, 2351538388135125
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..800
Programs
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Maple
with(numtheory): d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]): a:= proc(n) option remember; `if`(n<2, 0, a(n-2)*n+doublefactorial(n-2)*d(n)) end: seq(a(n), n=0..40); -
Mathematica
d[n_] := n*Sum[i[[2]]*PrimePi[i[[1]]]/i[[1]], {i, FactorInteger[n]}]; a[n_] := a[n] = If[n < 2, 0, a[n-2]*n + (n-2)!!*d[n]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 02 2022, after Alois P. Heinz *)