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

0,6

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

Formula

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

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 *)

Crossrefs

First differences of A001190.

Sequence in context: A215109 A131322 A224747 * A047761 A349055 A026786

Adjacent sequences: A036654 A036655 A036656 * A036658 A036659 A036660

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved