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%I #5 Aug 18 2015 09:03:47
%S 1,1,9,105,7665,303345,25893945,1765268505,345763843425,
%T 42813526781025,9399638261838825,1573582072888650825,
%U 563295733721953657425,139523356060051359020625,55722660999371761475705625,17053184982967015188566885625,9496879931794641573011009810625
%N Number of permutations p of [2n] without fixed points such that p^8 = Id.
%H Alois P. Heinz, <a href="/A261428/b261428.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) = (2n)! * [x^(2n)] exp(x^2/2+x^4/4+x^8/8).
%p b:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
%p add(mul(n-i, i=1..j-1)*b(n-j), j=[2,4,8])))
%p end:
%p a:= n-> b(2*n):
%p seq(a(n), n=0..20);
%Y Bisection of column k=8 of A261430.
%Y Cf. A053498.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 18 2015