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 A036657 Number of n-node rooted unlabeled trees with out-degree <=2 and exactly 2 edges at the root. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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. 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 A026786 A027246 Adjacent sequences:  A036654 A036655 A036656 * A036658 A036659 A036660 KEYWORD nonn AUTHOR STATUS approved

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Last modified September 28 08:33 EDT 2020. Contains 337394 sequences. (Running on oeis4.)