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A261431
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Number of permutations p of [n] without fixed points such that p^n = Id.
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4
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1, 0, 1, 2, 9, 24, 175, 720, 7665, 42560, 436401, 3628800, 70215145, 479001600, 7116730335, 88966701824, 1653438211425, 20922789888000, 457688776369825, 6402373705728000, 145083396337080201, 2457732174030848000, 55735573291977790575, 1124000727777607680000
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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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a(n) = n! * [x^n] exp(Sum_{d|n, d>1} x^d/d).
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MAPLE
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with(numtheory):
A:= proc(n, k) option remember; `if`(n<0, 0, `if`(n=0, 1,
add(mul(n-i, i=1..j-1)*A(n-j, k), j=divisors(k) minus {1})))
end:
a:= n-> A(n$2):
seq(a(n), n=0..25);
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MATHEMATICA
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A[n_, k_] := A[n, k] = If[n < 0, 0, If[n == 0, 1, Sum[Product[n - i, {i, 1, j - 1}] A[n - j, k], {j, Divisors[k] ~Complement~ {1}}]]];
a[n_] := A[n, n];
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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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