A036657 Number of n-node rooted unlabeled trees with out-degree <=2 and exactly 2 edges at the root.

0, 0, 0, 1, 1, 3, 5, 12, 23, 52, 109, 244, 532, 1196, 2671, 6055, 13726, 31380, 71901, 165635, 382610, 887215, 2062777, 4810230, 11243898, 26346341, 61863991, 145560102, 343121676, 810246372, 1916417479, 4539722153, 10769366928, 25582243781, 60847034869

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2500
• S. J. Cyvin, J. Brunvoll, B. N. Cyvin, Enumeration of constitutional isomers of polyenes, J. Molec. Struct. (Theochem) 357, no. 3 (1995) 255-261.
• Index entries for sequences related to rooted trees

Crossrefs

First differences of A001190.

Programs

Maple

N := 40: G036657 := series(G001190*(1/x-1)-1,x,N); A036657 := n->coeff(G036657,x,n);

Mathematica

terms = 36; A[_] = 0;
Do[A[x_] = x + (1/2) (A[x]^2 + A[x^2]) + O[x]^terms // Normal, {terms}];
CoefficientList[1 + A[x], x] // Differences (* Jean-François Alcover, Oct 24 2019 *)

Formula

G.f. satisfies A(x) = (W(x)-x)*(1-x)/x-x, where W(x) is g.f. for A001190.