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A120815
Number of permutations of length n with exactly 7 occurrences of the pattern 2-13.
4
42, 1664, 33338, 468200, 5253864, 50442128, 431645370, 3380738400, 24682378500, 170201240352, 1119398566704, 7074531999584, 43215257135312, 256343213520000, 1482127305153560, 8378542979807616, 46428426576857886
OFFSET
7,1
REFERENCES
R. Parviainen, Lattice path enumeration of permutations with k occurrences of the pattern 2-13, preprint, 2006.
Robert 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.
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) = (n+5)*(40320 + 67824*n - 20180*n^2 - 7556*n^3 - 5*n^4 + 211*n^5 + 25*n^6 + n^7)*binomial(2*n, n-7)/(5040*(n+8)*(n+9)).
G.f.: x^7*C^15*(132 + 16516*C - 92666*C^2 + 215944*C^3 - 281094*C^4 + 225628*C^5 - 110922*C^6 + 25360*C^7 + 7066*C^8 - 9364*C^9 + 4622*C^10 - 1440*C^11 + 294*C^12 - 36*C^13 + 2*C^14)/(2-C)^13, where C=(1-sqrt(1-4*x))/(2*x) is the Catalan function.
CROSSREFS
Column k=7 of A263776.
Sequence in context: A000502 A215545 A004997 * A162879 A163225 A163743
KEYWORD
nonn,easy
AUTHOR
Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 06 2006; definition corrected Feb 08 2008
STATUS
approved