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A102736 Number of permutations of n elements without cycles whose length is a multiple of 3. 4
1, 1, 2, 4, 16, 80, 400, 2800, 22400, 179200, 1792000, 19712000, 216832000, 2818816000, 39463424000, 552487936000, 8839806976000, 150276718592000, 2554704216064000, 48539380105216000, 970787602104320000, 19415752042086400000, 427146544925900800000, 9824370533295718400000, 225960522265801523200000, 5649013056645038080000000, 146874339472770990080000000, 3818732826292045742080000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Differs from A247007 first at n=27. - Alois P. Heinz, Sep 09 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

FORMULA

E.g.f.: (1-x^3)^(1/3)/(1-x).

a(n) ~ n! * 3^(1/3) / (GAMMA(2/3) * n^(1/3)). - Vaclav Kotesovec, Mar 15 2014

EXAMPLE

G.f. = 1 + x + 2*x^2 + 4*x^3 + 16*x^4 + 80*x^5 + 400*x^6 + 2800*x^7 + ...

MAPLE

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

      irem(j, 3)=0, 0, a(n-j)*(j-1)!*binomial(n-1, j-1)), j=1..n))

    end:

seq(a(n), n=0..27);  # Alois P. Heinz, Jul 31 2017

MATHEMATICA

nn=21; a=Sum[x^n/n, {n, 3, nn, 3}]; Range[0, nn]!CoefficientList[Series[Exp[Log[1/(1-x)]-a], {x, 0, nn}], x]  (* Geoffrey Critzer, Nov 11 2012 *)

a[ n_] := If[ n < 0, 0, n! With[{m = Quotient[n, 3]}, (-1)^m Binomial[-2/3, m]]]; (* Michael Somos, Aug 05 2016 *)

PROG

(PARI) {a(n) = my(m); if( n<0, 0, m = n\3; n! * (-1)^m * binomial(-2/3, m))}; /* Michael Somos, Aug 05 2016 */

CROSSREFS

Cf. A000090, A000246.

Sequence in context: A275555 A058926 A340900 * A247007 A103619 A027436

Adjacent sequences:  A102733 A102734 A102735 * A102737 A102738 A102739

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 08 2005

STATUS

approved

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Last modified May 10 22:15 EDT 2021. Contains 343780 sequences. (Running on oeis4.)