%I #18 Jul 02 2019 02:56:16
%S 1,1,1,1,4,16,136,736,4096,20224,326656,2970496,33826816,291237376,
%T 2129910784,13607197696,324498374656,4599593353216,52741679343616,
%U 495632154179584,7127212838772736,94268828128854016,2098358019107700736,34030412427789500416
%N Number of degree-n even permutations of order dividing 8.
%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="/A061131/b061131.txt">Table of n, a(n) for n = 0..502</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.
%H T. Koda, M. Sato, Y. Tskegahara, <a href="http://dx.doi.org/10.1142/S0219498815500528">2-adic properties for the numbers of involutions in the alternating groups</a>, J. Algebra Appl. 14 (2015), no. 4, 1550052 (21 pages).
%F E.g.f.: 1/2*exp(x + 1/2*x^2 + 1/4*x^4 + 1/8*x^8) + 1/2*exp(x - 1/2*x^2 - 1/4*x^4 - 1/8*x^8).
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(1/2*exp(x + 1/2*x^2 + 1/4*x^4 + 1/8*x^8) + 1/2*exp(x - 1/2*x^2 - 1/4*x^4 - 1/8*x^8))) \\ _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