cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A211774 #23 Mar 18 2018 15:45:28
%S A211774 0,0,0,3,12,60,420,3255,28056,270144,2868840,33293205,419329020,
%T A211774 5697423732,83069039508,1293734268645,21436030749840,376516868504160,
%U A211774 6988441065717744,136675039085498691,2809247116432575420,60543293881318183740,1365186080156105513460
%N A211774 Number of rooted 2-regular labeled graphs on n nodes.
%H A211774 Alois P. Heinz, <a href="/A211774/b211774.txt">Table of n, a(n) for n = 0..170</a>
%F A211774 a(n) = n*A001205(n).
%F A211774 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 A211774 a(n) ~ sqrt(2) * n^(n+1) / exp(n+3/4). - _Vaclav Kotesovec_, Aug 22 2014
%p A211774 egf:= x *diff(exp(-x/2-x^2/4)/sqrt(1-x), x):
%p A211774 a:= n-> n! * coeff(series(egf, x, n+1), x, n):
%p A211774 seq(a(n), n=0..30);  # _Alois P. Heinz_, May 18 2012
%t A211774 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 A211774 nonn
%O A211774 0,4
%A A211774 _Geoffrey Critzer_, May 18 2012