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A211774 Number of rooted 2-regular labeled graphs on n nodes. 1

%I

%S 0,0,0,3,12,60,420,3255,28056,270144,2868840,33293205,419329020,

%T 5697423732,83069039508,1293734268645,21436030749840,376516868504160,

%U 6988441065717744,136675039085498691,2809247116432575420,60543293881318183740,1365186080156105513460

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

%H Alois P. Heinz, <a href="/A211774/b211774.txt">Table of n, a(n) for n = 0..170</a>

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

%F 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.

%F a(n) ~ sqrt(2) * n^(n+1) / exp(n+3/4). - _Vaclav Kotesovec_, Aug 22 2014

%p egf:= x *diff(exp(-x/2-x^2/4)/sqrt(1-x), x):

%p a:= n-> n! * coeff(series(egf, x, n+1), x, n):

%p seq(a(n), n=0..30); # _Alois P. Heinz_, May 18 2012

%t 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]

%K nonn

%O 0,4

%A _Geoffrey Critzer_, May 18 2012

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Last modified January 20 23:20 EST 2019. Contains 319343 sequences. (Running on oeis4.)