cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A329053 Number of bicolored acyclic graphs on n unlabeled nodes.

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%I A329053 #9 Nov 05 2019 05:52:29
%S A329053 1,2,4,8,16,32,65,134,280,598,1300,2884,6516,15008,35147,83680,202139,
%T A329053 494982,1226753,3074146,7779561,19863702,51125018,132541616,345867101,
%U A329053 907922596,2396276355,6355845398,16934718359,45309972502,121697068925,328029259192
%N A329053 Number of bicolored acyclic graphs on n unlabeled nodes.
%C A329053 The two color classes are not interchangeable. Adjacent nodes cannot have the same color.
%H A329053 Andrew Howroyd, <a href="/A329053/b329053.txt">Table of n, a(n) for n = 0..500</a>
%F A329053 Euler transform of A122086.
%o A329053 (PARI)
%o A329053 EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A329053 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 A329053 seq(n)={concat([1], EulerT(Vec(2*TreeGf(n) - TreeGf(n)^2)))}
%Y A329053 Antidiagonal sums of A329052.
%Y A329053 Cf. A122086.
%K A329053 nonn
%O A329053 0,2
%A A329053 _Andrew Howroyd_, Nov 02 2019