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

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