A061132 - OEIS

%I #18 Jul 02 2019 02:56:27

%S 1,1,1,1,4,40,190,610,1660,13420,174700,1326700,30818800,342140800,

%T 2534931400,16519411000,143752426000,4842417082000,73620307162000,

%U 687934401562000,17165461784680000,308493094924720000,4585953613991980000,53843602355379220000

%N Number of degree-n even permutations of order dividing 10.

%D J. Riordan, An Introduction to Combinatorial Analysis, John Wiley & Sons, Inc. New York, 1958 (Chap 4, Problem 22).

%H Alois P. Heinz, <a href="/A061132/b061132.txt">Table of n, a(n) for n = 0..491</a>

%H Lev Glebsky, Melany Licón, Luis Manuel Rivera, <a href="https://arxiv.org/abs/1907.00548">On the number of even roots of permutations</a>, arXiv:1907.00548 [math.CO], 2019.

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

%e For n=4 the a(4)=4 solutions are (1), (1, 2)(3, 4), (1, 3)(2, 4), (1, 4)(2, 3) (permutations in cyclic notation). - _Luis Manuel Rivera Martínez_, Jun 18 2019

%t With[{nn = 22}, CoefficientList[Series[1/2 Exp[x + x^2/2 + x^5/5 + x^10/10] + 1/2 Exp[x - x^2/2 + x^5/5 - x^10/10], {x, 0, nn}], x]* Range[0, nn]!] (* _Luis Manuel Rivera Martínez_, Jun 18 2019 *)

%o (PARI) my(x='x+O('x^25)); Vec(serlaplace(1/2*exp(x + 1/2*x^2 + 1/5*x^5 + 1/10*x^10) + 1/2*exp(x - 1/2*x^2 + 1/5*x^5 - 1/10*x^10))) \\ _Michel Marcus_, Jun 18 2019

%Y Cf. A000085, A001470, A001472, A052501, A053496-A053505, A001189, A001471, A001473, A061121-A061128, A000704, A061129-A061132, A048099, A051695, A061133-A061135.

%K easy,nonn

%O 0,5

%A _Vladeta Jovovic_, Apr 14 2001