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 A294783 Number of trees with n bicolored nodes and f nodes of the first color. Triangle T(n,f) read by rows, 0<=f<=n. 7
 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 4, 6, 4, 2, 3, 9, 15, 15, 9, 3, 6, 20, 43, 51, 43, 20, 6, 11, 48, 116, 175, 175, 116, 48, 11, 23, 115, 329, 573, 698, 573, 329, 115, 23, 47, 286, 918, 1866, 2626, 2626, 1866, 918, 286, 47, 106, 719, 2609, 5978, 9656, 11241, 9656, 5978, 2609, 719, 106, 235, 1842 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1274 FORMULA T(n,f) = T(n,n-f), flipping all node colors. EXAMPLE The triangle starts     1;     1,   1;     1,   1,   1;     1,   2,   2,    1;     2,   4,   6,    4,    2;     3,   9,  15,   15,    9,    3;     6,  20,  43,   51,   43,   20,    6;    11,  48, 116,  175,  175,  116,   48,  11;    23, 115, 329,  573,  698,  573,  329, 115,  23;    47, 286, 918, 1866, 2626, 2626, 1866, 918, 286, 47;   106, 719,2609, 5978, 9656,11241, 9656,5978,2609,719,106;   235,1842, 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=(1+y)*x*Ser(R(n, y))); 1 + B - (B^2 - substvec(B, [x, y], [x^2, y^2]))/2} { my(A=M(10)); for(n=0, #A-1, print(Vecrev(polcoeff(A, n)))) } \\ Andrew Howroyd, May 12 2018 CROSSREFS Cf. A038056 (row sums), A000055 (diagonal and 1st column), A000081 (subdiagonal and 2nd column), A303833 (3rd column), A303843 (4th column), A304311 (connected graphs), A304489 (rooted). Sequence in context: A294600 A247495 A230290 * A172021 A325182 A215959 Adjacent sequences:  A294780 A294781 A294782 * A294784 A294785 A294786 KEYWORD nonn,tabl AUTHOR R. J. Mathar, Apr 16 2018 EXTENSIONS Row 10 completed. - R. J. Mathar, Apr 29 2018 STATUS approved

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Last modified May 11 03:20 EDT 2021. Contains 343784 sequences. (Running on oeis4.)