A120813 Number of permutations of length n with exactly 5 occurrences of the pattern 2-13.

0, 0, 0, 0, 0, 12, 352, 5392, 59670, 541044, 4285127, 30772896, 205200710, 1291195620, 7754735430, 44827592160, 251003101440, 1368033658992, 7285815623268, 38033923266368, 195107105534280, 985573624414808, 4911044001390648

Offset

1,6

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.

Formula

a(n) = ((n+4)(-108 - 192 n +3 n^2 + 8 n^3 + n^4))/(120(n + 7))binomial[2n, n - 6]; generating function = x^6 C^13 (-14 - 540C + 1519C^2 - 1517C^3 + 616C^4 + 70C^5 - 199C^6 + 97C^7 - 22C^8 + 2C^9)/(2-C)^9, where C=(1-Sqrt[1-4x])/(2x) is the Catalan function.

Crossrefs

Cf. A002629, A094218, A094219, A120812, A120814-A120816.

Column k=5 of A263776.

Sequence in context: A171206 A219407 A203148 * A202926 A134800 A053068

Adjacent sequences: A120810 A120811 A120812 * A120814 A120815 A120816

Keyword

nonn

Author

Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 06 2006, entries corrected Feb 08 2008

Status

approved