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A005772 Number of permutations of length n with 2 cycle lengths.
(Formerly M2978)
6
3, 14, 95, 424, 3269, 21202, 178443, 1622798, 17064179, 177093256, 2293658861, 29296367476, 416567286225, 6250052633294, 103272943796399, 1717954871163982, 32068960264609523, 601640759502181648, 12257756112146028309, 257187849583000601516 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
H. S. Wilf, Three problems in combinatorial asymptotics, J. Combin. Theory, A 35 (1983), 199-207.
MAPLE
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):
seq(a(n), n=0..30); # Alois P. Heinz, Feb 01 2014
MATHEMATICA
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 *)
CROSSREFS
Column k=2 of A218868.
Sequence in context: A091906 A214378 A094369 * A233083 A053984 A113181
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Nov 02 2003
STATUS
approved

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Last modified March 28 16:00 EDT 2024. Contains 371254 sequences. (Running on oeis4.)