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A122086 Number of unlabeled free bicolored trees with n nodes (the colors are not interchangeable).

%I A122086 #11 Nov 03 2019 01:42:52
%S A122086 2,1,2,3,6,10,22,42,94,203,470,1082,2602,6270,15482,38525,97258,
%T A122086 247448,635910,1645411,4289010,11245670,29656148,78595028,209273780,
%U A122086 559574414,1502130920,4046853091,10939133170,29661655793
%N A122086 Number of unlabeled free bicolored trees with n nodes (the colors are not interchangeable).
%D A122086 R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
%H A122086 Andrew Howroyd, <a href="/A122086/b122086.txt">Table of n, a(n) for n = 1..500</a>
%F A122086 For n even, a(n) = 2*A000055(n) - A000081(n/2), for n odd, a(n) = 2*A000055(n).
%F A122086 G.f.: 2*f(x) - f(x)^2 where f(x) is the g.f. of A000081. - _Andrew Howroyd_, Nov 02 2019
%o A122086 (PARI) \\ here TreeGf is A000081 as g.f.
%o A122086 TreeGf(N)={my(A=vector(N, j, 1)); for (n=1, N-1, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d*A[d]) * A[n-k+1] ) ); x*Ser(A)}
%o A122086 seq(n)={Vec(2*TreeGf(n) - TreeGf(n)^2)} \\ _Andrew Howroyd_, Nov 02 2019
%Y A122086 Row sums of A122085.
%Y A122086 Antidiagonal sums of A329054.
%Y A122086 Same as A125702 except for n = 1.
%Y A122086 Cf. A000055, A000081.
%K A122086 nonn
%O A122086 1,1
%A A122086 _N. J. A. Sloane_, Oct 19 2006
%E A122086 Edited by _Christian G. Bower_ and _Franklin T. Adams-Watters_, Jan 05 2007