OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..300
FORMULA
a(n) = (1/2)*n*(n-1)*I(n-2) for n>=2, where I(n)=A000085(n) is the number of involutions of {1,2,...,n}.
Rec. rel.: a(n) = [n/(n-2)][a(n-1) + (n-1)a(n-2)], a(1)=0, a(2)=1.
E.g.f.: x^2/2 * exp(x+x^2/2).
a(n) ~ sqrt(2)/4 * n^(n/2+1)*exp(sqrt(n)-n/2-1/4) * (1-17/(24*sqrt(n))). - Vaclav Kotesovec, Aug 15 2013
EXAMPLE
a(3) = 3 because in (1)(2)(3), (1)(23), (12)(3), (13)(2) we have three 2-cycles.
MAPLE
a[1] := 0: a[2] := 1: for n from 3 to 27 do a[n] := n*(a[n-1]+(n-1)*a[n-2])/(n-2) end do: seq(a[n], n = 1 .. 27);
MATHEMATICA
Range[0, 20]! CoefficientList[ Series[x^2/2 Exp[x+x^2/2], {x, 0, 20}], x] // Rest
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jul 22 2009
STATUS
approved