A261429 Number of permutations p of [3n] without fixed points such that p^9 = Id.

1, 2, 40, 42560, 17987200, 8116908800, 43924225945600, 108050180446208000, 215140299047145472000, 2906668948375666073600000, 21059302309493030917734400000, 112131367456110324265700556800000, 2891761281909068919518711775232000000

Offset: 0

Author

Alois P. Heinz, Aug 18 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..165

Crossrefs

Trisection of column k=9 of A261430.

Cf. A053499.

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=[3,9])))
    end:
a:= n-> b(3*n):
seq(a(n), n=0..15);

Formula

a(n) = (3n)! * [x^(3n)] exp(x^3/3+x^9/9).