A119857 Number of equicolored (unrooted) trees on 2n nodes.

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

Andrew Howroyd, Table of n, a(n) for n = 1..100

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.

Cf. A119855, A119856.

Sequence in context: A184265 A020041 A081891 * A305654 A241465 A320488

Adjacent sequences: A119854 A119855 A119856 * A119858 A119859 A119860

Keyword

nonn

Author

N. J. A. Sloane, Aug 04 2006

Extensions

Terms a(8) and beyond from Andrew Howroyd, May 21 2018

Status

approved