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 A128816 Number of partitions of an n-element set avoiding the pattern 12|3. 0
 1, 1, 2, 4, 8, 19, 53, 160, 512, 1753, 6431, 25072, 103022, 444145, 2004281, 9447784, 46407476, 236950873, 1254862955, 6880495528, 38999582018, 228195894313, 1376543144453, 8550048509440, 54619642413848, 358490894378881, 2415134218161767, 16686051606437104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS A. M. Goyt, Avoidance of partitions of a 3-element set, arXiv:math/0603481 [math.CO], 2006-2007 FORMULA a(0)=1, a(1)=1, a(n) = 1 + a(n-1) + Sum_{k=1..n-2} binomial(n-2, k)*a(n-k-2). The e.g.f. satisfies the differential eqution y'' = y' + y(e^x-1) + e^x. CROSSREFS Sequence in context: A269023 A173310 A320178 * A006897 A287025 A034767 Adjacent sequences:  A128813 A128814 A128815 * A128817 A128818 A128819 KEYWORD nonn AUTHOR Ralf Stephan, May 08 2007 STATUS approved

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Last modified May 27 12:01 EDT 2020. Contains 334657 sequences. (Running on oeis4.)