A120816 Number of permutations of length n with exactly 8 occurrences of the pattern 2-13.

9, 716, 20466, 365996, 4939341, 55098294, 535240680, 4680045630, 37665984798, 283492037268, 2018852205700, 13724440760376, 89682252682256, 566388685336800, 3472428372731880, 20740959695100150, 121059468257664984

Offset: 7

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 = 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.

Crossrefs

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

Column k=8 of A263776.

Formula

a(n) = (-7983360 - 12956832n + 10475400n^2 + 3647724n^3 - 416326n^4 - 249417n^5 - 19971n^6 + 2646n^7 + 576n^8 + 39n^9 + n^10)/(40320(n+8)(n+9)(n+10))Binomial[2n, n-7]; generating function = x^7 C^15(29 - 65536C + 499576C^2 - 1679496C^3 + 3298054C^4 - 4270444C^5 + 3911698C^6 - 2671744C^7 + 1439239C^8 - 659504C^9 + 279446C^10 - 112922C^11 + 41165C^12 - 12362C^13 + 2816C^14 - 448C^15 + 44C^16 - 2C^17)/(2-C)^15, where C=(1-Sqrt[1-4x])/(2x) is the Catalan function.