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A346066
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Sum of GCD of cycle lengths over all permutations of [n].
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2
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0, 1, 3, 10, 45, 216, 1505, 9360, 84105, 730240, 7715169, 76204800, 1090114025, 11975040000, 185501455425, 2791872219136, 45361870178625, 690452066304000, 14415096609538625, 236887827111936000, 5448878874163974249, 108418310412206080000, 2381309423564793710625
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} k * A346085(n,k).
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EXAMPLE
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a(3) = 10 = 3+3+1+1+1+1: (123), (132), (1)(23), (13)(2), (12)(3), (1)(2)(3).
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MAPLE
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b:= proc(n, g) option remember; `if`(n=0, g, add((j-1)!
*b(n-j, igcd(g, j))*binomial(n-1, j-1), j=1..n))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..24);
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MATHEMATICA
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b[n_, g_] := b[n, g] = If[n == 0, g, Sum[(j - 1)!*
b[n - j, GCD[g, j]]*Binomial[n - 1, j - 1], {j, 1, n}]];
a[n_] := b[n, 0];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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