A241982 Number of endofunctions on [2n] where the largest cycle length equals n.

1, 3, 93, 8600, 1719060, 604727424, 331079253120, 260480095349760, 278592031202284800, 388855261570122547200, 686533182382689959116800, 1495779844806108697677004800, 3942052104672989614027181260800, 12360865524060039746012601384960000

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..198

Formula

a(n) = A241981(2n,n).

a(n) ~ 2^(3*n+1/2) * n^(2*n-1) / exp(n). - Vaclav Kotesovec, Aug 19 2014

Example

a(1) = 3: (1,1), (1,2), (2,2).

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
      b(n-i*j, i-1), j=0..n/i)))
    end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, min(j, k)), j=0..n):
a:= n-> `if`(n=0, 1, A(2*n, n) -A(2*n, n-1)):
seq(a(n), n=0..15);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = Which[n==0, 1, i<1, 0, True, Sum[(i-1)!^j* multinomial[n, Join[{n-i*j}, Table[i, {j}]]]/j!*b[n-i*j, i-1], {j, 0, n/i} ] ];
A[n_, k_] := Sum[Binomial[n-1, j-1]*n^(n-j)*b[j, Min[j, k]], {j, 0, n}];
a[n_] := If[n == 0, 1, A[2n, n] - A[2n, n-1]];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Apr 01 2017, translated from Maple *)

Crossrefs

Cf. A241981, A246050.

Sequence in context: A288070 A116292 A139543 * A037113 A142887 A297489

Adjacent sequences: A241979 A241980 A241981 * A241983 A241984 A241985

Keyword

nonn

Author

Alois P. Heinz, Aug 10 2014

Status

approved