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 A249632 Triangular array read by rows.  T(n,k) is the number of labeled trees with black and white nodes having exactly k black nodes, n>=0, 0<=k<=n. 0
 1, 1, 1, 1, 2, 1, 3, 9, 9, 3, 16, 64, 96, 64, 16, 125, 625, 1250, 1250, 625, 125, 1296, 7776, 19440, 25920, 19440, 7776, 1296, 16807, 117649, 352947, 588245, 588245, 352947, 117649, 16807, 262144, 2097152, 7340032, 14680064, 18350080, 14680064, 7340032, 2097152, 262144 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums = A038058. T(n,n) = T(n,0) = n^(n-2) free trees A000272. T(n,n-1) = T(n,1) = n^(n-1) rooted trees A000169. T(n,2) = A081131. REFERENCES F. Harary and E. Palmer, Graphical Enumeration, Academic Press,1973, page 30, exercise 1.10. LINKS FORMULA E.g.f.: A(x + y*x) where A(x) is the e.g.f. for A000272. EXAMPLE 1, 1,    1, 1,    2,    1, 3,    9,    9,     3, 16,   64,   96,    64,    16, 125,  625,  1250,  1250,  625,   125, 1296, 7776, 19440, 25920, 19440, 7776, 1296 MATHEMATICA nn = 6; f[x_] := Sum[n^(n - 2) x^n/n!, {n, 1, nn}]; Map[Select[#, # > 0 &] &,   Range[0, nn]! CoefficientList[     Series[f[x + y x] + 1, {x, 0, nn}], {x, y}]] // Grid CROSSREFS Sequence in context: A249456 A234746 A237765 * A126009 A301282 A246063 Adjacent sequences:  A249629 A249630 A249631 * A249633 A249634 A249635 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Nov 02 2014 STATUS approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)