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%I #16 Oct 24 2019 10:22:13
%S 0,0,0,1,1,3,5,12,23,52,109,244,532,1196,2671,6055,13726,31380,71901,
%T 165635,382610,887215,2062777,4810230,11243898,26346341,61863991,
%U 145560102,343121676,810246372,1916417479,4539722153,10769366928,25582243781,60847034869
%N Number of n-node rooted unlabeled trees with out-degree <=2 and exactly 2 edges at the root.
%H Alois P. Heinz, <a href="/A036657/b036657.txt">Table of n, a(n) for n = 0..2500</a>
%H S. J. Cyvin, J. Brunvoll, B. N. Cyvin, <a href="https://doi.org/10.1016/0166-1280(95)04329-6">Enumeration of constitutional isomers of polyenes</a>, J. Molec. Struct. (Theochem) 357, no. 3 (1995) 255-261.
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F G.f. satisfies A(x) = (W(x)-x)*(1-x)/x-x, where W(x) is g.f. for A001190.
%p N := 40: G036657 := series(G001190*(1/x-1)-1,x,N); A036657 := n->coeff(G036657,x,n);
%t terms = 36; A[_] = 0;
%t Do[A[x_] = x + (1/2) (A[x]^2 + A[x^2]) + O[x]^terms // Normal, {terms}];
%t CoefficientList[1 + A[x], x] // Differences (* _Jean-François Alcover_, Oct 24 2019 *)
%Y First differences of A001190.
%K nonn
%O 0,6
%A _N. J. A. Sloane_.
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