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A119857
Number of equicolored (unrooted) trees on 2n nodes.
4
1, 1, 4, 14, 65, 316, 1742, 10079, 61680, 391473, 2565262, 17237962, 118341446, 827194809, 5872518213, 42256545977, 307681822711, 2263881127801, 16813356777456, 125917441081662, 950148951332802, 7218810159035143, 55187741462110393, 424318236236124092
OFFSET
1,3
COMMENTS
For precise definition, recurrence and asymptotics see the Pippenger reference.
LINKS
N. Pippenger, Enumeration of equicolorable trees, SIAM J. Discrete Math., 14 (2001), 93-115.
PROG
(PARI) \\ R is b.g.f of rooted trees x nodes, y in one part
R(n)={my(A=O(x)); for(j=1, 2*n, A = if(j%2, 1, y)*x*exp(sum(i=1, j, 1/i * subst(subst(A + x * O(x^(j\i)), x, x^i), y, y^i)))); A};
seq(n)={my(A=Pol(R(n))); my(r(x, y)=substvec(A, ['x, 'y], [x, y/x])); Vec(polcoeff((r(x, y/x) + r(y/x, x) - r(x, y/x)*r(y/x, x)), 0) + O(y*y^n))} \\ Andrew Howroyd, May 23 2018
CROSSREFS
Main diagonal of A329054.
Sequence in context: A184265 A020041 A081891 * A305654 A241465 A320488
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 04 2006
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, May 21 2018
STATUS
approved