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

0,2

Links

Table of n, a(n) for n=0..27.

Index entries for sequences related to trees

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.

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 *)

Crossrefs

Essentially the same as A036250. Cf. A038054.

Sequence in context: A129012 A136122 A121875 * A176022 A316275 A113031

Adjacent sequences: A036248 A036249 A036250 * A036252 A036253 A036254

Keyword

nonn

Author

Christian G. Bower, Nov 15 1998

Status

approved