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

Author

N. J. A. Sloane, Aug 04 2006

Keywords

• nonn

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.

Crossrefs

Main diagonal of A329054.

Cf. A119855, A119856.

Programs

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

Extensions

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