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 A008295 Triangle of numbers of point labeled rooted trees. 1
 1, 1, 1, 1, 2, 2, 2, 5, 9, 9, 4, 13, 34, 64, 64, 9, 35, 119, 326, 625, 625, 20, 95, 401, 1433, 4016, 7776, 7776, 48, 262, 1316, 5799, 21256, 60387, 117649, 117649, 115, 727, 4247, 22224, 100407, 373895, 1071904, 2097152, 2097152 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(n, m) where n counts the vertices and 0 <= m <= n counts the labels. - Sean A. Irvine, Mar 22 2018 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 134. LINKS Sean A. Irvine, Table of n, a(n) for n = 0..527 J. Riordan, The numbers of labeled colored and chromatic trees, Acta Mathematica 97 (1957) 211. FORMULA G.f. r(x,y) = T(n,m) * y^m * x^n / m! satisfies r(x,y) * exp(r(x)) = (1+y) * r(x) * exp(r(x,y)) where r(x) is the o.g.f. for A000081. - Sean A. Irvine, Mar 22 2018 CROSSREFS Cf. A000081 (T(n,0)), A000107 (T(n,1)), A000169 (T(n,n)), A000524 (T(n,2)), A000444 (T(n,3)), A000525 (T(n,4)). Sequence in context: A208050 A039886 A109523 * A216694 A116697 A014244 Adjacent sequences:  A008292 A008293 A008294 * A008296 A008297 A008298 KEYWORD nonn,tabl,nice AUTHOR EXTENSIONS More terms from Sean A. Irvine, Mar 22 2018 STATUS approved

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Last modified July 16 06:19 EDT 2018. Contains 312654 sequences. (Running on oeis4.)