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 A185650 a(n) is the number of rooted trees with 2n vertices n of whom are leaves. 1
 1, 2, 8, 39, 214, 1268, 7949, 51901, 349703, 2415348, 17020341, 121939535, 885841162, 6511874216, 48359860685, 362343773669, 2736184763500, 20805175635077, 159174733727167, 1224557214545788, 9467861087020239, 73534456468877012, 573484090227222260 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 V. M. Kharlamov and S. Yu. Orevkov, The number of trees half of whose vertices are leaves and asymptotic enumeration of plane real algebraic curves, J. of Combinatorial Theory, Ser. A, 105 (2004), 127-142 MATHEMATICA terms = 23; m = 2 terms; T[_, _] = 0; Do[T[x_, z_] = z x - x + x Exp[Sum[Series[1/k T[x^k, z^k], {x, 0, j}, {z, 0, j}], {k, 1, j}]] // Normal, {j, 1, m}]; cc = CoefficientList[#, z]& /@ CoefficientList[T[x, z] , x]; Table[cc[[2n+1, n+1]], {n, 1, terms}] (* Jean-François Alcover, Sep 14 2018 *) PROG (PARI) \\ here R is A055277 as vector of polynomials R(n) = {my(A = O(x)); for(j=1, n, A = x*(y - 1  + exp( sum(i=1, j, 1/i * subst( subst( A + x * O(x^(j\i)), x, x^i), y, y^i) ) ))); Vec(A)}; {my(A=R(2*30)); vector(#A\2, k, polcoeff(A[2*k], k))} \\ Andrew Howroyd, May 21 2018 CROSSREFS Cf. A000081, A055277. Sequence in context: A218321 A236339 A292100 * A059275 A020047 A231496 Adjacent sequences:  A185647 A185648 A185649 * A185651 A185652 A185653 KEYWORD nonn AUTHOR Stepan Orevkov, Aug 29 2013 EXTENSIONS Terms a(20) and beyond from Andrew Howroyd, May 21 2018 STATUS approved

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Last modified September 17 12:57 EDT 2019. Contains 327131 sequences. (Running on oeis4.)