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Number of degree-n permutations of order exactly 10.
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%I #10 May 27 2016 08:43:18

%S 0,0,0,0,0,0,504,4032,27216,514080,4823280,57081024,500972472,

%T 4412103696,60619398840,686638592640,9335025764064,104304736815552,

%U 1180585704051936,29016515871665280,478096386437121480

%N Number of degree-n permutations of order exactly 10.

%F 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).

%F From _Benedict W. J. Irwin_, May 27 2016: (Start)

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

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

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

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

%F 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,

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

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

%F (End)

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

%K easy,nonn

%O 1,7

%A _Vladeta Jovovic_, Apr 14 2001