A120815 Number of permutations of length n with exactly 7 occurrences of the pattern 2-13.

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

Alois P. Heinz, Table of n, a(n) for n = 7..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) = ((n+5)(40320 + 67824n - 20180n^2 - 7556n^3 - 5n^4 + 211n^5 + 25n^6 + n^7)/(5040(n+8)(n+9))Binomial[2n, n-7]; generating function = x^7 C^15(32 + 16516C - 92666C^2 + 215944C^3 - 281094C^4 + 225628C^5 - 110922C^6 + 25360C^7 + 7066C^8 - 9364C^9 + 4622C^10 - 1440C^11 + 294C^12 - 36C^13 + 2C^14)/(2-C)^13, where C=(1-Sqrt[1-4x])/(2x) is the Catalan function.

Crossrefs

Cf. A002629, A094218, A094219, A120812-A120814, A120816.

Column k=7 of A263776.

Sequence in context: A000502 A215545 A004997 * A162879 A163225 A163743

Adjacent sequences: A120812 A120813 A120814 * A120816 A120817 A120818

Keyword

nonn

Author

Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 06 2006; definition corrected Feb 08 2008

Status

approved