A036251 - OEIS

%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