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A261317
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Number of permutations sigma of [n] without fixed points such that sigma^6 = Id.
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7
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1, 0, 1, 2, 3, 20, 175, 210, 4585, 24920, 101745, 1266650, 13562395, 48588540, 1082015935, 9135376250, 63098660625, 1069777108400, 13628391601825, 88520971388850, 2134604966569075, 23945393042070500, 236084869688242575, 4893567386193135650, 72576130763294383225
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f.: exp(x^2*(x^4+2*x+3)/6).
D-finite with recurrence a(n) +(-n+1)*a(n-2) -(n-1)*(n-2)*a(n-3) -(n-5)*(n-1)*(n-2)*(n-3)*(n-4)*a(n-6)=0. - R. J. Mathar, Jul 04 2023
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EXAMPLE
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a(4) = 3: 2143, 3412, 4321.
a(5) = 20: 21453, 21534, 23154, 24513, 25431, 31254, 34152, 34521, 35124, 35412, 41523, 43251, 43512, 45132, 45213, 51432, 53214, 53421, 54123, 54231.
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MAPLE
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a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
add(mul(n-i, i=1..j-1)*a(n-j), j=[2, 3, 6])))
end:
seq(a(n), n=0..30);
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MATHEMATICA
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a[n_] := a[n] = If[n < 0, 0, If[n == 0, 1, Sum[Product[n - i, {i, 1, j - 1}]*a[n - j], {j, {2, 3, 6}}]]];
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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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