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A339651 Number of trees with n integer labeled leaves spanning an initial interval of positive integers and all non-leaf nodes having degree 3.

%I A339651 #8 Jan 10 2021 12:41:57
%S A339651 1,1,2,4,14,92,884,11200,175460,3264456,70251004,1715832180,
%T A339651 46881727360,1416695166888,46909359288468,1688908328539092,
%U A339651 65689047712686678,2744769306400145168,122618498876673122160,5832010466617354498700,294228096306408399225374
%N A339651 Number of trees with n integer labeled leaves spanning an initial interval of positive integers and all non-leaf nodes having degree 3.
%H A339651 Andrew Howroyd, <a href="/A339651/b339651.txt">Table of n, a(n) for n = 0..200</a>
%o A339651 (PARI) \\ here U(n,k) is k-th column of A339650 as a vector.
%o A339651 R(n, k)={my(v=vector(n)); v[1]=k; for(n=2, n, v[n]=sum(j=1, (n-1)\2, v[j]*v[n-j]) + if(n%2, 0, binomial(v[n/2]+1, 2))); v}
%o A339651 U(n, k)={my(g=x*Ser(R(n,k))); Vec(1 + g + (subst(g + O(x*x^(n\3)), x, x^3) - g^3)/3) }
%o A339651 seq(n)={sum(k=0, n, U(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)) )}
%Y A339651 Row sums of A339650.
%Y A339651 Cf. A319590 (rooted).
%K A339651 nonn
%O A339651 0,3
%A A339651 _Andrew Howroyd_, Dec 14 2020