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

1,7

Links

Table of n, a(n) for n=1..21.

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)

Crossrefs

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

Sequence in context: A259953 A180164 A263286 * A141145 A253724 A166763

Adjacent sequences: A061121 A061122 A061123 * A061125 A061126 A061127

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 14 2001

Status

approved