A120814 Number of permutations of length n with exactly 6 occurrences of the pattern 2-13.

0, 0, 0, 0, 0, 2, 140, 3262, 47802, 535990, 5038418, 41781432, 315447990, 2214289350, 14664659100, 92612930280, 562220244768, 3301016862024, 18836205435208, 104862661271840, 571336322754792, 3054404571541092, 16056744308319000

Offset: 1

Author

Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 06 2006

Keywords

• nonn

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 = 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.

Crossrefs

Cf. A002629, A094218, A094219, A120812-A120813, A120815-A120816.

Column k=6 of A263776.

Formula

a(n) = (20160 + 44448n + 548n^2 - 4196n^3 - 565n^4 + 67n^5 + 17n^6 + n^7)/(720(n+7)(n+6))binomial[2n, n-6]; generating function = x^6 C^13 (-42 + 4054C - 18354C^2 + 36038C^3 - 40660C^4 + 30080C^5 - 16090C^6 + 6914C^7 - 2604C^8 + 840C^9 - 202C^10 + 30C^11 - 2C^12)/(2-C)^11, where C=(1-Sqrt[1-4x])/(2x) is the Catalan function.