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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
OFFSET
1,5
REFERENCES
R. Lie, Permutations and Patterns, Master's Thesis, Goeteborg, Sweden: Chalmers University of Technology, 2004.
LINKS
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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, May 27 2004
STATUS
approved