# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a094219 Showing 1-1 of 1 %I A094219 #23 Sep 08 2022 08:45:13 %S A094219 0,0,0,0,7,112,1092,8400,56100,341088,1939938,10498488,54679625, %T A094219 276276000,1362040680,6580248480,31256180280,146350008000, %U A094219 676868787000,3097351569312,14042319855102,63144549413792,281895309883000 %N A094219 Number of permutations of length n with exactly 3 occurrences of the pattern 2-13. %D A094219 R. Lie, Permutations and Patterns, Master's Thesis, Goeteborg, Sweden: Chalmers University of Technology, 2004. %H A094219 Alois P. Heinz, Table of n, a(n) for n = 1..500 %H A094219 R. Parviainen, Lattice Path Enumeration of Permutations with k Occurrences of the Pattern 2-13, Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.2. %F A094219 a(n) = (1/3)*binomial(n+2,2)*binomial(2*n,n-5). %F A094219 G.f.: (-7*x^2+8*x-2-(4*x^7+14*x^6+84*x^5-350*x^4+350*x^3-147*x^2+28*x-2) /(1-4*x)^(5/2)) /(2*x^5). - _Mark van Hoeij_, Apr 30 2013 %t A094219 Table[Binomial[n + 2, 2] Binomial[2 n, n - 5]/3, {n, 1, 30}] (* _Vincenzo Librandi_, Aug 20 2015 *) %o A094219 (PARI) a(n)=1/3*binomial(n+2,2)*binomial(2*n,n-5) %o A094219 (Magma) [(1/3)*Binomial(n+2,2)*Binomial(2*n,n-5): n in [1..30]]; // _Vincenzo Librandi_, Aug 20 2015 %Y A094219 Cf. A094218. %Y A094219 Column k=3 of A263776. %K A094219 nonn %O A094219 1,5 %A A094219 _Benoit Cloitre_, May 27 2004 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE