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A120813 Number of permutations of length n with exactly 5 occurrences of the pattern 2-13. 4
0, 0, 0, 0, 0, 12, 352, 5392, 59670, 541044, 4285127, 30772896, 205200710, 1291195620, 7754735430, 44827592160, 251003101440, 1368033658992, 7285815623268, 38033923266368, 195107105534280, 985573624414808, 4911044001390648 (list; graph; refs; listen; history; text; internal format)
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
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
Column k=5 of A263776.
Sequence in context: A171206 A219407 A203148 * A202926 A134800 A053068
KEYWORD
nonn
AUTHOR
Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 06 2006, entries corrected Feb 08 2008
STATUS
approved

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Last modified May 23 17:39 EDT 2024. Contains 372765 sequences. (Running on oeis4.)