%I A027852
%S A027852 0,1,1,3,6,16,37,96,239,622,1607,4235,11185,29862,80070,216176,
%T A027852 586218,1597578,4370721,12003882,33077327,91433267,253454781,
%U A027852 704429853,1962537755,5479855546,15332668869,42983656210
%N A027852 Number of connected functions on n points with a loop of length 2.
%C A027852 Also rooted trees on n+1 nodes where root has degree 2.
%H A027852 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A027852 G.f.: A(x) = (B(x)^2 + B(x^2))/2 where B(x) is g.f. of A000081.
%p A027852 b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), 
               k=1..n-1)/(n-1) fi end: s:= proc(n,k) option remember; add(b(n+1-j*k), 
               j=1..iquo(n,k)) end: B:= proc(n) option remember; unapply (add (b(k)*x^k, 
               k=1..n),x) end: a:= n-> coeff (series ((B(n-1)(x)^2 +B(n-1)(x^2))/
               2, x=0, n+1), x,n): seq (a(n), n=1..28); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 22 2008]
%Y A027852 Cf. A000081, A000226, A001372, A002861.
%Y A027852 Sequence in context: A130095 A072824 A089406 this_sequence A114410 A096588 
               A073079
%Y A027852 Adjacent sequences: A027849 A027850 A027851 this_sequence A027853 A027854 
               A027855
%K A027852 nonn
%O A027852 1,4
%A A027852 Christian G. Bower (bowerc(AT)usa.net), Dec 14 1997
%E A027852 Edited by Christian G. Bower (bowerc(AT)usa.net), Feb 12 2002