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A261317 Number of permutations sigma of [n] without fixed points such that sigma^6 = Id. 7
1, 0, 1, 2, 3, 20, 175, 210, 4585, 24920, 101745, 1266650, 13562395, 48588540, 1082015935, 9135376250, 63098660625, 1069777108400, 13628391601825, 88520971388850, 2134604966569075, 23945393042070500, 236084869688242575, 4893567386193135650, 72576130763294383225 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

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

EXAMPLE

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

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

MAPLE

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

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

    end:

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

MATHEMATICA

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}}]]];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Jun 10 2018, from Maple *)

CROSSREFS

Column k=6 of A261430.

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

Sequence in context: A013340 A218873 A012416 * A177946 A006246 A110372

Adjacent sequences:  A261314 A261315 A261316 * A261318 A261319 A261320

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 14 2015

STATUS

approved

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Last modified February 27 06:03 EST 2020. Contains 332299 sequences. (Running on oeis4.)