Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Feb 19 2018 03:36:41
%S 0,1,1,3,9,29,105,390,1528,6119,25140,104936,444637,1905331,8246619,
%T 35988793,158199975,699788234,3112679085,13913394416,62465305846,
%U 281551756181,1273583739390,5779693081500,26306751243309
%N Number of unlabeled PQ-trees with n leaves.
%C A PQ-tree is a rooted tree with P-type internal nodes that have at least 3 children that are reversibly ordered (the reverse of the order is equivalent to the order) and Q-type internal nodes that have at least 2 unordered children.
%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 242 (3.3.91).
%H Christian G. Bower, <a href="/A136628/b136628.txt">Table of n, a(n) for n = 0..511</a>
%H <a href="/transforms_pari.txt">Transforms in PARI</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F G.f. satisfies: A(x) = x + (2-A(x)^2)/(2-2A(x)^2) + (1+A(x))*A(x^2)/(2-2A(x^2)) + exp(Sum_{i>=1} A(x^i)/i) - (A(x)^2+A(x^2))/2 - 2A(x) - 2.
%o (PARI) read("transforms_pari.txt"); {pqu(A) = A = trv_chain(A)+trv_euler(A)-trv_euler_2(A)-2*A; A[1]=0; A} {apqu(n) = local(SX,SY); SY = SX = [0,1]; for(i=1,n,SY=concat(SY,0);SX=concat(SX,0);SY=SX+pqu(SY)); SY} A136628(n) = apqu(min(1,n-1))[n+1]
%K nonn
%O 0,4
%A _Christian G. Bower_, Jan 14 2008