The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A094219 Number of permutations of length n with exactly 3 occurrences of the pattern 2-13. 8
 0, 0, 0, 0, 7, 112, 1092, 8400, 56100, 341088, 1939938, 10498488, 54679625, 276276000, 1362040680, 6580248480, 31256180280, 146350008000, 676868787000, 3097351569312, 14042319855102, 63144549413792, 281895309883000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 REFERENCES R. Lie, Permutations and Patterns, Master's Thesis, Goeteborg, Sweden: Chalmers University of Technology, 2004. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..500 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. FORMULA a(n) = (1/3)*binomial(n+2,2)*binomial(2*n,n-5). 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 MATHEMATICA Table[Binomial[n + 2, 2] Binomial[2 n, n - 5]/3, {n, 1, 30}] (* Vincenzo Librandi, Aug 20 2015 *) PROG (PARI) a(n)=1/3*binomial(n+2, 2)*binomial(2*n, n-5) (Magma) [(1/3)*Binomial(n+2, 2)*Binomial(2*n, n-5): n in [1..30]]; // Vincenzo Librandi, Aug 20 2015 CROSSREFS Cf. A094218. Column k=3 of A263776. Sequence in context: A061233 A117795 A163700 * A212702 A217223 A067404 Adjacent sequences: A094216 A094217 A094218 * A094220 A094221 A094222 KEYWORD nonn AUTHOR Benoit Cloitre, May 27 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 08:12 EST 2023. Contains 367515 sequences. (Running on oeis4.)