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A005772
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Number of permutations of length n with 2 cycle lengths.
(Formerly M2978)
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6
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3, 14, 95, 424, 3269, 21202, 178443, 1622798, 17064179, 177093256, 2293658861, 29296367476, 416567286225, 6250052633294, 103272943796399, 1717954871163982, 32068960264609523, 601640759502181648, 12257756112146028309, 257187849583000601516
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OFFSET
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3,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MAPLE
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with(numtheory): with(combinat):
a:= n-> add(add(add((i-1)!^j*(d-1)!^((n-i*j)/d)*
multinomial(n, i$j, d$((n-i*j)/d))/j!/((n-i*j)/d)!,
d=select(x->x<i, divisors(n-i*j))), j=1..n/i), i=2..n-1):
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MATHEMATICA
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multinomial[n_, k_List] := n!/Times @@ (k!); a[n_] := Sum[Sum[Sum[(i - 1)!^j*(d-1)!^((n-i*j)/d)*multinomial[n, Join[Array[i&, j], Array[d&, ((n - i*j)/d)]]]/j!/((n-i*j)/d)!, {d, Select[If[n == i*j, {}, Divisors[n - i*j]], #<i&]}], {j, 1, n/i}], {i, 2, n-1}]; Table[a[n], {n, 3, 30}] (* Jean-François Alcover, Nov 12 2015, 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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EXTENSIONS
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STATUS
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approved
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