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%I #12 Jan 10 2020 13:13:12
%S 1,1,4,14,65,316,1742,10079,61680,391473,2565262,17237962,118341446,
%T 827194809,5872518213,42256545977,307681822711,2263881127801,
%U 16813356777456,125917441081662,950148951332802,7218810159035143,55187741462110393,424318236236124092
%N Number of equicolored (unrooted) trees on 2n nodes.
%C For precise definition, recurrence and asymptotics see the Pippenger reference.
%H Andrew Howroyd, <a href="/A119857/b119857.txt">Table of n, a(n) for n = 1..100</a>
%H N. Pippenger, <a href="http://dx.doi.org/10.1137/S0895480100368463">Enumeration of equicolorable trees</a>, SIAM J. Discrete Math., 14 (2001), 93-115.
%o (PARI) \\ R is b.g.f of rooted trees x nodes, y in one part
%o 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};
%o 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
%Y Main diagonal of A329054.
%Y Cf. A119855, A119856.
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Aug 04 2006
%E Terms a(8) and beyond from _Andrew Howroyd_, May 21 2018
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