A119855 - OEIS

%I #10 May 23 2018 16:26:03

%S 1,2,9,44,249,1506,9687,64803,447666,3169566,22897260,168168164,

%T 1252391041,9437809359,71850420813,551876468717,4272100488830,

%U 33299732401378,261165251593743,2059638535690473,16324255856903830,129969379170062142,1039056925387672998

%N Number of equicolorable rooted trees on 2n nodes.

%C For precise definition, recurrence and asymptotics see the Pippenger reference.

%C An equicolorable tree is a tree which can be colored with two colors with adjacent nodes having different colors and there being an equal number of nodes of each color. - _Andrew Howroyd_, May 21 2018

%D N. Pippenger, Enumeration of equicolorable trees, SIAM J. Discrete Math., 14 (2001), 93-115.

%H Andrew Howroyd, <a href="/A119855/b119855.txt">Table of n, a(n) for n = 1..100</a>

%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), 0) + O(y*y^n))} \\ _Andrew Howroyd_, May 23 2018

%Y Cf. A119856, A119857.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Aug 04 2006

%E Terms a(8) and beyond from _Andrew Howroyd_, May 21 2018