A036251 Number of trees with 2-colored leaves.

1, 2, 3, 3, 7, 14, 35, 85, 231, 633, 1845, 5461, 16707, 51945, 164695, 529077, 1722279, 5664794, 18813369, 62996850, 212533226, 721792761, 2466135375, 8471967938, 29249059293, 101440962296, 353289339927, 1235154230060

Offset: 0

Author

Christian G. Bower, Nov 15 1998

Keywords

• nonn

Links

• Index entries for sequences related to trees

Crossrefs

Essentially the same as A036250. Cf. A038054.

Programs

Mathematica

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 *)

Formula

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.