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 A071075 Number of permutations that avoid the generalized pattern 132-4. 9
 1, 1, 2, 6, 23, 107, 585, 3671, 25986, 204738, 1776327, 16824237, 172701135, 1909624371, 22626612450, 285982186662, 3840440707485, 54603776221965, 819424594880559, 12942757989763101, 214626518776190178, 3728112755679416898, 67692934780306842501, 1282399636333412178531, 25303124674163685176793 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..460 Juan S. Auli, Pattern Avoidance in Inversion Sequences, Ph. D. thesis, Dartmouth College, ProQuest Dissertations Publishing (2020), 27964164. Juan S. Auli and Sergi Elizalde, Consecutive Patterns in Inversion Sequences, arXiv:1904.02694 [math.CO], 2019. See Table 1. Andrew M. Baxter, Algorithms for Permutation Statistics, Ph. D. Dissertation, Rutgers University, May 2011. Andrew M. Baxter, Algorithms for Permutation Statistics, Ph. D. Dissertation, Rutgers University, May 2011. Andrew M. Baxter and Lara K. Pudwell, Enumeration schemes for dashed patterns, arXiv:1108.2642 [math.CO], 2011. Sergey Kitaev, Partially Ordered Generalized Patterns, preprint. Sergey Kitaev, Partially Ordered Generalized Patterns, Discrete Math. 298 (2005), no. 1-3, 212-229. FORMULA E.g.f.: exp(int(A(y), y=0..x)), where A(y) = 1/(1 - int(exp(-t^2/2), t=0..y)). a(n) ~ c * d^n * n! / n^f, where d = 1/A240885 = 1/(sqrt(2)*InverseErf(sqrt(2/Pi))) = 0.7839769312035474991242486548698125357473282..., f = 1.2558142944089303287268746534354522944538722816671534535062816..., c = 0.2242410644782853722452053227678681810005068... . - Vaclav Kotesovec, Aug 23 2014 Let b(n) = A111004(n) = number of permutations of [n] that avoid the consecutive pattern 132. Then a(n) = Sum_{i = 0..n-1} binomial(n-1,i)*b(i)*a(n-1-i) with a(0) = b(0) = 1. [See the recurrence for A_n and B_n in the proof of Theorem 13 in Kitaev's papers.] - Petros Hadjicostas, Nov 01 2019 MAPLE A(y) := 1/(1-int(exp(-t^2/2), t=0..y)); B(x) := exp(int(A(y), y=0..x)); series(B(x), x=0, 30); MATHEMATICA CoefficientList[Series[E^(Integrate[1/(1-Integrate[E^(-t^2/2), {t, 0, y}]), {y, 0, x}]), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Aug 23 2014 *) PROG (PARI) N=66; x='x+O('x^N); A=1/(1-intformal(exp(-x^2/2))); egf=exp(intformal(A)); Vec(serlaplace(egf)) \\ Joerg Arndt, Aug 28 2014 CROSSREFS Cf. A071088, A071076, A071077, A111004. Sequence in context: A336071 A200403 A113226 * A007555 A101053 A155857 Adjacent sequences:  A071072 A071073 A071074 * A071076 A071077 A071078 KEYWORD nonn AUTHOR Sergey Kitaev (kitaev(AT)math.chalmers.se), May 26 2002 EXTENSIONS Link and a(11)-a(20) from Andrew Baxter, May 17 2011 Typo in first formula corrected by Vaclav Kotesovec, Aug 23 2014 STATUS approved

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Last modified October 5 17:43 EDT 2022. Contains 357261 sequences. (Running on oeis4.)