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 A106236 Triangle of the numbers of different forests with m rooted trees having distinct orders. 1
 1, 1, 0, 2, 1, 0, 4, 2, 0, 0, 9, 6, 0, 0, 0, 20, 13, 2, 0, 0, 0, 48, 37, 4, 0, 0, 0, 0, 115, 86, 17, 0, 0, 0, 0, 0, 286, 239, 46, 0, 0, 0, 0, 0, 0, 719, 577, 142, 8, 0, 0, 0, 0, 0, 0, 1842, 1607, 367, 18, 0, 0, 0, 0, 0, 0, 0, 4766, 4025, 1136, 76, 0, 0, 0, 0, 0, 0, 0, 0, 12486, 11185 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) = 0 if and only if n < m + (((1+m)*m - 1)^2 -1)/8, where m is the number of trees in the forests counted by a(n). LINKS FORMULA a(n)= sum over the partitions of N:1K1+2K2+ ... +NKN, with exactly m distinct parts, of product_{1=0} (1+y*A000081(k)*x^k). - Vladeta Jovovic, May 14 2005 EXAMPLE a(3)=0 because m = 2 and (see comments) 3 < (2 + 3). a(4)>0 because m = 1. Note that (((1+m)*m - 1)^2 -1)/8 = 0, if m = 1. It is clear that n >= m. CROSSREFS Cf. A106234, A000081. Sequence in context: A166555 A136329 A122073 * A122792 A139136 A138002 Adjacent sequences:  A106233 A106234 A106235 * A106237 A106238 A106239 KEYWORD nonn,tabl,changed AUTHOR Washington Bomfim, Apr 28 2005 STATUS approved

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