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A055814 E.g.f: exp(x^3/3+x^2/2)-1. 2
0, 1, 2, 3, 20, 55, 210, 1225, 4760, 26145, 157850, 811195, 5345340, 35170135, 222472250, 1650073425, 12000388400, 88563700225, 720929459250, 5786843137075, 48072795270500, 424314078763575, 3731123025279650 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) is the number of n-permutations in which all cycles have length two or three. [From Geoffrey Critzer, Feb 21 2010]

REFERENCES

Miklos Bona, A Walk Through Combinatorics, World Scientific Publishing Co., 2002, page 169. [From Geoffrey Critzer, Feb 21 2010]

LINKS

Table of n, a(n) for n=1..23.

FORMULA

a(n)=subs(x=0, diff(exp(x^3/3+x^2/2), x$n)), n=1, 2...

a(n)=(n-1)*a(n-2) + (n-1)*(n-2)*a(n-3). [Joerg Arndt, Oct 02 2009]

a(n) ~ n^(2*n/3)*exp(1/18-2*n/3-n^(1/3)/6+n^(2/3)/2)/sqrt(3) * (1 + 49/(324*n^(1/3)) - 72451/(1049760*n^(2/3))). - Vaclav Kotesovec, Jun 26 2013

EXAMPLE

a(4)= 3 because there are 3 permutations of {1,2,3,4} that have cycle length two or three: (1,2)(3,4);(1,3)(2,4);(1,4)(2,3). [From Geoffrey Critzer, Feb 21 2010]

MATHEMATICA

Drop[CoefficientList[Series[Exp[x^2/2 + x^3/3], {x, 0, 20}], x]* Table[n!, {n, 0, 20}], 1] [From Geoffrey Critzer, Feb 21 2010]

CROSSREFS

Cf. A081096.

Cf. A001470, A000085. [Joerg Arndt, Oct 02 2009]

Sequence in context: A195686 A072472 A233410 * A151370 A041567 A087301

Adjacent sequences:  A055811 A055812 A055813 * A055815 A055816 A055817

KEYWORD

nonn

AUTHOR

Karol A. Penson, Mar 05 2003

EXTENSIONS

Improved definition as proposed by Joerg Arndt - R. J. Mathar, Oct 23 2009

STATUS

approved

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Last modified March 28 19:06 EDT 2017. Contains 284246 sequences.