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A070945 Number of permutations on n letters that have only cycles of length 4 or less. 2
1, 1, 2, 6, 24, 96, 456, 2472, 14736, 92304, 632736, 4661856, 36364032, 297668736, 2583425664, 23550535296, 224086162176, 2221083839232, 22976670905856, 246829966447104, 2745834333566976, 31605782067081216, 376290722808502272 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Dennis P. Walsh, The Number of Permutations with Only Small Cycles, preprint [From Geoffrey Critzer, May 24 2009]

LINKS

Table of n, a(n) for n=0..22.

I. Mezo, Periodicity of the last digits of some combinatorial sequences, arXiv preprint arXiv:1308.1637 [math.CO], 2013 and J. Int. Seq. 17 (2014) #14.1.1 .

R. Petuchovas, Asymptotic analysis of the cyclic structure of permutations, arXiv:1611.02934 [math.CO], p. 6, 2016.

FORMULA

E.g.f.: exp(x + 1/2*x^2 + 1/3*x^3 + 1/4*x^4).

MAPLE

with (combstruct):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, m>=card))}, labeled]; end: A:=a(4):seq(count(A, size=n), n=0..22); # Zerinvary Lajos, Jun 11 2008

G := exp(x+(1/2)*x^2+(1/3)*x^3+(1/4)*x^4): seq(factorial(n)*coeftayl(G, x = 0, n), n = 0 .. 22); # Emeric Deutsch, Jun 21 2009

MATHEMATICA

Table[Sum[Binomial[n, 4 i]*(4 i)!/(i!*4^i)* Sum[Binomial[n - 4 i, 3 j]*(3 j)!/(j!*3^j)* Sum[Binomial[n - 4 i - 3 j, 2 k]*(2 k)!/(k!*2^k), {k, 0, n}], {j, 0, n}], {i, 0, n}], {n, 0, 22}] (* Geoffrey Critzer, May 24 2009 *)

CROSSREFS

Cf. A057693.

Sequence in context: A147912 A147903 A147895 * A152320 A267384 A152327

Adjacent sequences:  A070942 A070943 A070944 * A070946 A070947 A070948

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and Sharon Sela, May 18 2002

STATUS

approved

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Last modified December 13 15:03 EST 2018. Contains 318086 sequences. (Running on oeis4.)