A261428 Number of permutations p of [2n] without fixed points such that p^8 = Id.

1, 1, 9, 105, 7665, 303345, 25893945, 1765268505, 345763843425, 42813526781025, 9399638261838825, 1573582072888650825, 563295733721953657425, 139523356060051359020625, 55722660999371761475705625, 17053184982967015188566885625, 9496879931794641573011009810625

Offset: 0

Author

Alois P. Heinz, Aug 18 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250

Crossrefs

Bisection of column k=8 of A261430.

Cf. A053498.

Programs

Maple

b:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*b(n-j), j=[2,4,8])))
    end:
a:= n-> b(2*n):
seq(a(n), n=0..20);

Formula

a(n) = (2n)! * [x^(2n)] exp(x^2/2+x^4/4+x^8/8).