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A027616
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Number of permutations of n elements containing a 2-cycle.
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2
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0, 0, 1, 3, 9, 45, 285, 1995, 15855, 142695, 1427895, 15706845, 188471745, 2450132685, 34301992725, 514529890875, 8232476226975, 139952095858575, 2519137759913775, 47863617438361725, 957272348112505425, 20102719310362613925, 442259824841726816925, 10171975971359716789275
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..23.
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FORMULA
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E.g.f.: (1 - exp(-x^2/2)) / (1-x).
n! * { 1 - sum[ k=0..floor(n/2) ] (-1)^k / (2^k * k!) }.
a(n) + A000266(n) = n!. - Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 09 2003
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MATHEMATICA
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nn=20; Table[n!, {n, 0, nn}]-Range[0, nn]!CoefficientList[Series[Exp[-x^2/2]/(1-x), {x, 0, nn}], x] (* Geoffrey Critzer, Oct 20 2012 *)
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PROG
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(PARI)
a(n) = n! * (1 - sum(k=0, floor(n/2), (-1)^k / (2^k * k!) ) );
/* Joerg Arndt, Oct 20 2012 */
(PARI)
N=33; x='x+O('x^N);
v=Vec( 'a0 + serlaplace( (1-exp(-x^2/2))/(1-x) ) );
v[1]-='a0; v
/* Joerg Arndt, Oct 20 2012 */
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CROSSREFS
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Sequence in context: A038059 A174318 A004990 * A013492 A106341 A065407
Adjacent sequences: A027613 A027614 A027615 * A027617 A027618 A027619
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KEYWORD
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nonn
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AUTHOR
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Joe Keane (jgk(AT)jgk.org)
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EXTENSIONS
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Added more terms, Geoffrey Critzer, Oct 20 2012
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STATUS
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approved
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