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A120816 Number of permutations of length n with exactly 8 occurrences of the pattern 2-13. 6
9, 716, 20466, 365996, 4939341, 55098294, 535240680, 4680045630, 37665984798, 283492037268, 2018852205700, 13724440760376, 89682252682256, 566388685336800, 3472428372731880, 20740959695100150, 121059468257664984 (list; graph; refs; listen; history; text; internal format)
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) = (-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.
CROSSREFS
Column k=8 of A263776.
Sequence in context: A332169 A282181 A053515 * A161585 A255259 A191367
KEYWORD
nonn
AUTHOR
Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 06 2006
STATUS
approved

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Last modified April 20 09:30 EDT 2024. Contains 371799 sequences. (Running on oeis4.)