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A212650 Number of permutations of n elements with at least one fixed point and at least one 2-cycle (transposition). 1
0, 0, 0, 3, 6, 25, 180, 1281, 10010, 90063, 902790, 9929755, 119134224, 1548768585, 21683033372, 325245031125, 5203916869710, 88466595897631, 1592398778725710, 30255576613653483, 605111531456405960, 12707342164389159945, 279561527629906821684 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

E.g.f.: (exp(x)-1)*(exp(x^2/2)-1)*exp(-x - x^2/2)/(1-x).

a(n) ~ n! * (exp(1)-1)*(exp(1/2)-1)*exp(-3/2) = n! * 0.248720059264354... - Vaclav Kotesovec, Aug 07 2013

EXAMPLE

a(3) = 3: 132, 213, 321.

a(4) = 6: 1243, 1324, 1432, 2134, 3214, 4231.

MATHEMATICA

nn=22; Range[0, nn]!CoefficientList[Series[(Exp[x]-1)(Exp[x^2/2]-1)Exp[-x-x^2/2]/(1-x), {x, 0, nn}], x]

CROSSREFS

Cf. A002467.

Sequence in context: A266549 A057730 A074432 * A297572 A137089 A197470

Adjacent sequences:  A212647 A212648 A212649 * A212651 A212652 A212653

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Feb 14 2013

STATUS

approved

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Last modified September 21 16:31 EDT 2021. Contains 347598 sequences. (Running on oeis4.)