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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

Index entries for sequences related to rooted trees

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-Fran├žois 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 15:51 EDT 2021. Contains 347478 sequences. (Running on oeis4.)