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A120812 Number of permutations of length n with exactly 4 occurrences of the pattern 2-13. 6
1, 44, 700, 7460, 63648, 470934, 3155691, 19660630, 115855025, 653392740, 3556757490, 18805317960, 97034823600, 490465092600, 2435567286708, 11910569958216, 57470522059594, 274051266477560, 1293219035408080 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

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 = 5..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) = (-36 - 100 m - 13 m^2 + 4 m^3 + m^4)/(24(m + 6))Binomial[2m, m - 5]; generating function = x^5 C^11 (5 - 118C + 259C^2 - 240C^3 + 142C^4 - 62C^5 + 17C^6 - 2 C^7)/(2-C)^7, where C=(1-Sqrt[1-4x])/(2x) is the Catalan function.

CROSSREFS

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

Column k=4 of A263776.

Sequence in context: A296649 A221505 A160066 * A282860 A232139 A296576

Adjacent sequences:  A120809 A120810 A120811 * A120813 A120814 A120815

KEYWORD

nonn

AUTHOR

Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 05 2006

STATUS

approved

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Last modified August 14 10:58 EDT 2022. Contains 356116 sequences. (Running on oeis4.)