

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
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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), 127142
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}] (* JeanFrançois 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



