%I #20 Jul 11 2018 10:36:51
%S 1,5,191,17519,2887921,742458253,273315477775,136025604432743,
%T 87816638377854497,71278145791452802133,70978809757898186241439,
%U 85023410230409691052228255,120545000629512292505954394769,199558149588334620585072909701981,381323441275017330119775857868585839
%N a(n) = A000085(4*n)/2^n.
%H Seiichi Manyama, <a href="/A316330/b316330.txt">Table of n, a(n) for n = 0..210</a>
%H S. Chowla, I. N. Herstein and W. K. Moore, <a href="http://dx.doi.org/10.4153/CJM-1951-038-3">On recursions connected with symmetric groups I</a>, Canad. J. Math. 3 (1951) 328-334.
%H Dongsu Kim and Jang Soo Kim, <a href="http://dx.doi.org/10.1016/j.jcta.2009.08.002">A combinatorial approach to the power of 2 in the number of involutions</a>, J. Comb. Theory Ser. A 117 (8) (2010): 1082-1094.
%Y Cf. A000085, A316331, A316332, A316333.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jul 09 2018, following a suggestion from _Doron Zeilberger_