A211774 Number of rooted 2-regular labeled graphs on n nodes.

0, 0, 0, 3, 12, 60, 420, 3255, 28056, 270144, 2868840, 33293205, 419329020, 5697423732, 83069039508, 1293734268645, 21436030749840, 376516868504160, 6988441065717744, 136675039085498691, 2809247116432575420, 60543293881318183740, 1365186080156105513460

Offset: 0

Author

Geoffrey Critzer, May 18 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..170

Programs

Maple

egf:= x *diff(exp(-x/2-x^2/4)/sqrt(1-x), x):
a:= n-> n! * coeff(series(egf, x, n+1), x, n):
seq(a(n), n=0..30);  # Alois P. Heinz, May 18 2012

Mathematica

nn = 20; a = Log[1/(1 - x)]/2 - x/2 - x^2/4; Drop[Range[0, nn]! CoefficientList[Series[x D[Exp[a], x], {x, 0, nn}], x], 3]

Formula

a(n) = n*A001205(n).

E.g.f.: x*A'(x) where A(x) = exp(-x/2-x^2/4)/sqrt(1-x) is the e.g.f. for A001205.

a(n) ~ sqrt(2) * n^(n+1) / exp(n+3/4). - Vaclav Kotesovec, Aug 22 2014