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

%I A061124 #10 May 27 2016 08:43:18
%S A061124 0,0,0,0,0,0,504,4032,27216,514080,4823280,57081024,500972472,
%T A061124 4412103696,60619398840,686638592640,9335025764064,104304736815552,
%U A061124 1180585704051936,29016515871665280,478096386437121480
%N A061124 Number of degree-n permutations of order exactly 10.
%F A061124 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 A061124 From _Benedict W. J. Irwin_, May 27 2016: (Start)
%F A061124 Let y1(0)=1, y1(1)=1,
%F A061124 Let -y1(n)-y1(n+1)+(n+2)*y1(n+2)=0,
%F A061124 Let y2(0)=1, y2(1)=1, y2(2)=1/2, y2(3)=1/6, y2(4)=1/24,
%F A061124 Let -y2(n)-y2(n+4)+(n+5)*y2(n+5)=0,
%F A061124 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 A061124 Let -y3(n)-y3(n+5)-y3(n+8)-y3(n+9)+(n+10)*y3(n+10)=0,
%F A061124 a(n) = 1+n!*(y3(n)-y2(n)-y1(n)).
%F A061124 (End)
%Y A061124 Cf. A000085, A001470, A001472, A052501, A053496-A053505, A001189, A001471, A001473, A061121-A061128.
%K A061124 easy,nonn
%O A061124 1,7
%A A061124 _Vladeta Jovovic_, Apr 14 2001