A120812 Number of permutations of length n with exactly 4 occurrences of the pattern 2-13.

1, 44, 700, 7460, 63648, 470934, 3155691, 19660630, 115855025, 653392740, 3556757490, 18805317960, 97034823600, 490465092600, 2435567286708, 11910569958216, 57470522059594, 274051266477560, 1293219035408080

Offset: 5

Author

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

Crossrefs

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

Column k=4 of A263776.

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.