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 A177483 Number of permutations avoiding the pattern 1231'. 4
 1, 1, 2, 6, 20, 85, 420, 2443, 16136, 120222, 993770, 9042451, 89725944, 964693717, 11168801294, 138549935190, 1833264311504, 25773751694161, 383664263687964, 6028473673565695, 99710105438401940, 1731651866118338766, 31505416776034601510, 599259743707431667279 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..460 Sergey Kitaev, Segmented partially ordered generalized patterns, Theoretical Computer Science 349(3) (2005), 420-428; see Proposition 7 (p. 424). FORMULA E.g.f.: x*exp(x/2) / (cos(sqrt(3)*x/2) - sin(sqrt(3)*x/2) / sqrt(3)) + 1. a(n) ~ n! * exp(Pi/(3*sqrt(3))) * (3*sqrt(3)/(2*Pi))^n. - Vaclav Kotesovec, Aug 24 2014 EXAMPLE For n = 4, we have a(4) = 20 because the only bad permutations are 1234, 1342, 1243 and 2341. MATHEMATICA CoefficientList[Series[x*E^(x/2)/(Cos[Sqrt[3]*x/2] - Sin[Sqrt[3]*x/2] / Sqrt[3]) + 1, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Aug 24 2014*) CROSSREFS Sequence in context: A177480 A365229 A089179 * A004104 A304932 A293032 Adjacent sequences: A177480 A177481 A177482 * A177484 A177485 A177486 KEYWORD nonn AUTHOR Signy Olafsdottir (signy06(AT)ru.is), May 09 2010, May 14 2010 EXTENSIONS Offset corrected by Vaclav Kotesovec, Aug 24 2014 More terms from Vaclav Kotesovec, Aug 24 2014 STATUS approved

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Last modified August 11 23:45 EDT 2024. Contains 375082 sequences. (Running on oeis4.)