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%I #11 Jul 06 2023 07:24:27
%S 1,3,12,60,345,2415,18480,166320,1596105,17557155,202951980,
%T 2638375740,35703612945,535554194175,8307234936000,141222993912000,
%U 2470641012464625,46942179236827875,914462992955011500
%N Number of degree-n permutations with exactly one even cycle.
%H Robert Israel, <a href="/A096471/b096471.txt">Table of n, a(n) for n = 2..449</a>
%F E.g.f.: -1/2*((1+x)/(1-x))^(1/2)*log(1-x^2).
%F Conjecture D-finite with recurrence a(n) -3*a(n-1) +(-2*n^2+8*n-3)*a(n-2) +(n-2)*(4*n-15)*a(n-3) +(n-3)*(n^3-9*n^2+22*n-7)*a(n-4) -(n-3)*(n-4)*(n-5)^2*a(n-5)=0. - _R. J. Mathar_, Jul 06 2023
%p S:= series(-1/2*((1+x)/(1-x))^(1/2)*log(1-x^2), x, 51):
%p seq(coeff(S,x,n)*n!, n=2..50); # _Robert Israel_, Nov 13 2017
%Y Cf. A060523, A028353.
%K easy,nonn
%O 2,2
%A _Vladeta Jovovic_, Aug 13 2004
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