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%I #5 Aug 18 2015 08:55:44
%S 1,2,40,42560,17987200,8116908800,43924225945600,108050180446208000,
%T 215140299047145472000,2906668948375666073600000,
%U 21059302309493030917734400000,112131367456110324265700556800000,2891761281909068919518711775232000000
%N Number of permutations p of [3n] without fixed points such that p^9 = Id.
%H Alois P. Heinz, <a href="/A261429/b261429.txt">Table of n, a(n) for n = 0..165</a>
%F a(n) = (3n)! * [x^(3n)] exp(x^3/3+x^9/9).
%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=[3,9])))
%p end:
%p a:= n-> b(3*n):
%p seq(a(n), n=0..15);
%Y Trisection of column k=9 of A261430.
%Y Cf. A053499.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Aug 18 2015
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