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 A302939 Number of signed trees with n nodes and p positive edges. Triangle T(n,p) read by rows, 0<=p
 1, 1, 1, 1, 1, 1, 2, 3, 3, 2, 3, 6, 9, 6, 3, 6, 16, 27, 27, 16, 6, 11, 37, 79, 96, 79, 37, 11, 23, 96, 233, 349, 349, 233, 96, 23, 47, 239, 679, 1187, 1439, 1187, 679, 239, 47, 106, 622, 1987, 4017, 5639, 5639, 4017, 1987, 622, 106, 235, 1607, 5784, 13216, 21263, 24758, 21263, 13216, 5784, 1607, 235 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 FORMULA T(n,p) = T(n,n-p-1), flipping all edge signs. EXAMPLE T(2,0)=T(2,1)=1: the tree on 2 nodes (one edge) has one variant with no positive edge and one variant with one positive edge. T(4,1)=3: the 2 trees on 4 nodes (three edges) have two variants from the linear tree with a positive edge (edge in the middle or at the end) and one variant from the star graph with one positive edge. T(5,0)=3: there are 3 trees on 5 nodes (4 edges) where all edges are negative. The triangle starts     1;     1,   1;     1,   1,   1;     2,   3,   3,    2;     3,   6,   9,    6,    3;     6,  16,  27,   27,   16,    6;    11,  37,  79,   96,   79,   37,  11;    23,  96, 233,  349,  349,  233,  96,  23;    47, 239, 679, 1187, 1439, 1187, 679, 239, 47;   106, 622,... PROG (PARI) R(n, y)={my(v=vector(n)); v[1]=1; for(k=1, n-1, my(p=(1+y)*v[k]); my(q=Vec(prod(j=0, poldegree(p, y), (1/(1-x*y^j) + O(x*x^(n\k)))^polcoeff(p, j)))); v=vector(n, j, v[j] + sum(i=1, (j-1)\k, v[j-i*k] * q[i+1]))); v; } M(n)={my(B=x*Ser(R(n, y))); B - (1+y)*(B^2 - substvec(B, [x, y], [x^2, y^2]))/2} { my(A=Vec(M(10))); for(n=1, #A, print(Vecrev(A[n]))) } \\ Andrew Howroyd, May 13 2018 CROSSREFS Cf. A000060 (row sums), A000055 (diagonal and 1st column), A027852 (subdiagonal and 2nd column), A304489 (rooted), A331113 (central coefficients). Sequence in context: A105612 A141744 A089783 * A090414 A068227 A235343 Adjacent sequences:  A302936 A302937 A302938 * A302940 A302941 A302942 KEYWORD nonn,tabl AUTHOR R. J. Mathar, Apr 16 2018 EXTENSIONS Completed row 10. - R. J. Mathar, Apr 29 2018 Terms a(58) and beyond from Andrew Howroyd, May 13 2018 STATUS approved

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Last modified June 1 02:09 EDT 2020. Contains 334758 sequences. (Running on oeis4.)