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 A261317 Number of permutations sigma of [n] without fixed points such that sigma^6 = Id. 7

%I

%S 1,0,1,2,3,20,175,210,4585,24920,101745,1266650,13562395,48588540,

%T 1082015935,9135376250,63098660625,1069777108400,13628391601825,

%U 88520971388850,2134604966569075,23945393042070500,236084869688242575,4893567386193135650,72576130763294383225

%N Number of permutations sigma of [n] without fixed points such that sigma^6 = Id.

%H Alois P. Heinz, <a href="/A261317/b261317.txt">Table of n, a(n) for n = 0..500</a>

%F E.g.f.: exp(x^2*(x^4+2*x+3)/6).

%e a(4) = 3: 2143, 3412, 4321.

%e a(5) = 20: 21453, 21534, 23154, 24513, 25431, 31254, 34152, 34521, 35124, 35412, 41523, 43251, 43512, 45132, 45213, 51432, 53214, 53421, 54123, 54231.

%p a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,

%p add(mul(n-i, i=1..j-1)*a(n-j), j=[2, 3, 6])))

%p end:

%p seq(a(n), n=0..30);

%t a[n_] := a[n] = If[n < 0, 0, If[n == 0, 1, Sum[Product[n - i, {i, 1, j - 1}]*a[n - j], {j, {2, 3, 6}}]]];

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jun 10 2018, from Maple *)

%Y Column k=6 of A261430.

%Y Cf. A001147, A052502, A052503, A052504, A053496, A261381.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Aug 14 2015

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Last modified April 5 14:44 EDT 2020. Contains 333245 sequences. (Running on oeis4.)