A061124 Number of degree-n permutations of order exactly 10.

0, 0, 0, 0, 0, 0, 504, 4032, 27216, 514080, 4823280, 57081024, 500972472, 4412103696, 60619398840, 686638592640, 9335025764064, 104304736815552, 1180585704051936, 29016515871665280, 478096386437121480

Offset: 1

Author

Vladeta Jovovic, Apr 14 2001

Keywords

• easy
• nonn

Crossrefs

Cf. A000085, A001470, A001472, A052501, A053496-A053505, A001189, A001471, A001473, A061121-A061128.

Formula

E.g.f.: exp(x) - exp(x+1/2*x^2) - exp(x+1/5*x^5) + exp(x+1/2*x^2+1/5*x^5+1/10*x^10).

From Benedict W. J. Irwin, May 27 2016: (Start)

Let y1(0)=1, y1(1)=1,

Let -y1(n)-y1(n+1)+(n+2)*y1(n+2)=0,

Let y2(0)=1, y2(1)=1, y2(2)=1/2, y2(3)=1/6, y2(4)=1/24,

Let -y2(n)-y2(n+4)+(n+5)*y2(n+5)=0,

Let y3(0)=1, y3(1)=1, y3(2)=1, y3(3)=2/3, y3(4)=5/12, y3(5)=5/12, y3(6)=11/36, y3(7)=31/126, y3(8)=307/2016, y3(9)=1643/18144,

Let -y3(n)-y3(n+5)-y3(n+8)-y3(n+9)+(n+10)*y3(n+10)=0,

a(n) = 1+n!*(y3(n)-y2(n)-y1(n)).

(End)