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A119856
Number of equicolorable (unrooted) trees on 2n nodes.
5
1, 1, 3, 9, 37, 168, 895, 5097, 30983, 196096, 1283552, 8621364, 59176966, 413613891, 2936303012, 21128390679, 153841228779, 1131941424480, 8406680733066, 62958726953945, 475074493277317, 3609405128045162, 27593870865196624, 212159118489924538, 1639760091688265416
OFFSET
1,3
COMMENTS
For precise definition, recurrence and asymptotics see the Pippenger reference.
LINKS
Austin Mohr, Unlabeled Trees
N. Pippenger, Enumeration of equicolorable trees, SIAM J. Discrete Math., 14 (2001), 93-115.
FORMULA
a(n) = (A000081(n) + A119857(n))/2. - Andrew Howroyd, May 21 2018
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) + r(y, y))/2} \\ Andrew Howroyd, May 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 04 2006
EXTENSIONS
a(8)-a(9) from John P. McSorley, Aug 08 2017
Terms a(10) and beyond from Andrew Howroyd, May 21 2018
STATUS
approved