A005772 Number of permutations of length n with 2 cycle lengths. (Formerly M2978)

3, 14, 95, 424, 3269, 21202, 178443, 1622798, 17064179, 177093256, 2293658861, 29296367476, 416567286225, 6250052633294, 103272943796399, 1717954871163982, 32068960264609523, 601640759502181648, 12257756112146028309, 257187849583000601516

Offset

3,1

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 3..200

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

Adjacent sequences: A005769 A005770 A005771 * A005773 A005774 A005775

Keyword

nonn

Author

Simon Plouffe

Extensions

More terms from Vladeta Jovovic, Nov 02 2003

Status

approved