A289950 Number of permutations of [n] having exactly two nontrivial cycles.

3, 35, 295, 2359, 19670, 177078, 1738326, 18607446, 216400569, 2721632121, 36842898989, 534442231933, 8273657327788, 136186274940140, 2375469940958988, 43774887758841996, 849887136894382191, 17340752094929572431, 370979946172969657107, 8304215235537338992931

Offset

4,1

Comments

A nontrivial cycle has size > 1.

Links

Alois P. Heinz, Table of n, a(n) for n = 4..450

Wikipedia, Permutation

Formula

E.g.f.: (log(1-x)+x)^2/2*exp(x).

-(n+1)*(n+2)*(n+3)*(n+4)*a(n)+(5+3*n)*(n+4)*(n+3)*(n+2)*a(n+1)-(n+4)*(n+3)*(3*n^2+15*n+16)*a(n+2)+(n+4)*(n^3+12*n^2+38*n+32)*a(n+3)-(2*n^3+18*n^2+48*n+35)*a(n+4)+(n+3)*(n+1)*a(n+5)=0. - Robert Israel, Mar 22 2018

Example

a(4) = 3: (12)(34), (13)(24), (14)(23).

Maple

S:= series((log(1-x)+x)^2/2*exp(x), x, 31):
seq(coeff(S, x, j)*j!, j=4..30); # Robert Israel, Mar 22 2018

Mathematica

Drop [Range[0, 30]! CoefficientList[Series[(Log[1 - x] + x)^2 / 2 Exp[x], {x, 0, 30}], x], 4] (* Vincenzo Librandi, Jul 22 2017 *)

Prog

(PARI) x='x+O('x^99); Vec(serlaplace((log(1-x)+x)^2/2*exp(x))) \\ Altug Alkan, Mar 22 2018

Crossrefs

Column k=2 of A136394.

Sequence in context: A069448 A339516 A121078 * A308033 A198961 A112488

Adjacent sequences: A289947 A289948 A289949 * A289951 A289952 A289953

Keyword

nonn

Author

Alois P. Heinz, Jul 16 2017

Status

approved