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%I #18 Jan 28 2019 14:00:24
%S 1,2,3,3,7,14,35,85,231,633,1845,5461,16707,51945,164695,529077,
%T 1722279,5664794,18813369,62996850,212533226,721792761,2466135375,
%U 8471967938,29249059293,101440962296,353289339927,1235154230060
%N Number of trees with 2-colored leaves.
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F G.f.: B(x) + B(x)^2/2 + B(x^2)/2 - B(x)*(B(x)-x), where B(x) is g.f. for A029856.
%t max = 30; B[_] = 1; Do[B[x_] = x*Exp[Sum[(B[x^k] + x^k)/k + O[x]^n, {k, 1, n}]] // Normal, {n, 1, max}]; A[x_] = 1 + x + x^2 + B[x] - B[x]^2/2 + B[x^2]/2; CoefficientList[A[x] + O[x]^max, x] (* _Jean-François Alcover_, Jan 28 2019 *)
%Y Essentially the same as A036250. Cf. A038054.
%K nonn
%O 0,2
%A _Christian G. Bower_, Nov 15 1998
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