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A261427 Number of permutations p of [7n] without fixed points such that p^7 = Id.

%I A261427 #7 Aug 18 2015 09:06:16
%S A261427 1,720,889574400,24825530695680000,5290995845684330496000000,
%T A261427 5123434663327851951402516480000000,
%U A261427 16586604100059403377645257954741452800000000,146550752102252281868362306608987740351496192000000000
%N A261427 Number of permutations p of [7n] without fixed points such that p^7 = Id.
%H A261427 Alois P. Heinz, <a href="/A261427/b261427.txt">Table of n, a(n) for n = 0..73</a>
%F A261427 a(n) = (7n)! * [x^(7n)] exp(x^7/7).
%p A261427 a:= proc(n) option remember; `if`(n=0, 1,
%p A261427       mul(7*n-i, i=1..6)*a(n-1))
%p A261427     end:
%p A261427 seq(a(n), n=0..10);
%Y A261427 7-section of column k=7 of A261430.
%Y A261427 Cf. A053497.
%K A261427 nonn
%O A261427 0,2
%A A261427 _Alois P. Heinz_, Aug 18 2015