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A246618
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Number of endofunctions on [2n] whose cycle lengths are multiples of n.
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2
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1, 4, 57, 4480, 866460, 302835456, 165589522560, 130247609057280, 139297568464454400, 194428045753727385600, 343266731083210449715200, 747889980460943180326502400, 1971026081420013638259189350400, 6180432779330984921337015828480000
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OFFSET
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0,2
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LINKS
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FORMULA
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MAPLE
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with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i=0 or i>n, 0, add(b(n-i*j, i+k, k)*(i-1)!^j*
multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
end:
a:= n->add(b(j, n$2)*(2*n)^(2*n-j)*binomial(2*n-1, j-1), j=0..2*n):
seq(a(n), n=0..15);
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MATHEMATICA
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multinomial[n_, k_] := n!/Times @@ (k!); b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0 || i > n, 0, Sum[b[n - i*j, i + k, k]*(i - 1)!^j * multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!, {j, 0, n/i}]]]; a[0] = 1; a[n_] := Sum[b[j, n, n]*(2n)^(2n-j)*Binomial[2n-1, j-1], {j, 0, 2n}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 26 2017, after Alois P. Heinz *)
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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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