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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. - Geoffrey Critzer, Feb 21 2010

REFERENCES

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

LINKS

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

FORMULA

a(n) = subs(x=0, (d^n/dx^n)exp(x^3/3 + x^2/2)), 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). - 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] (* Geoffrey Critzer, Feb 21 2010 *)

CROSSREFS

Cf. A081096.

Cf. A001470, A000085. - Joerg Arndt, Oct 02 2009

Sequence in context: A295365 A072472 A233410 * A151370 A041567 A087301

Adjacent sequences:  A055811 A055812 A055813 * A055815 A055816 A055817

KEYWORD

nonn,changed

AUTHOR

Karol A. Penson, Mar 05 2003

EXTENSIONS

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

STATUS

approved

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Last modified January 17 09:45 EST 2018. Contains 297815 sequences.