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 A120813 Number of permutations of length n with exactly 5 occurrences of the pattern 2-13. 4

%I

%S 0,0,0,0,0,12,352,5392,59670,541044,4285127,30772896,205200710,

%T 1291195620,7754735430,44827592160,251003101440,1368033658992,

%U 7285815623268,38033923266368,195107105534280,985573624414808,4911044001390648

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

%D R. Parviainen, Lattice path enumeration of permutations with k occurrences of the pattern 2-13, preprint, 2006.

%D 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.

%H Alois P. Heinz, <a href="/A120813/b120813.txt">Table of n, a(n) for n = 1..500</a>

%H R. Parviainen, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Parviainen/parviainen3.html">Lattice Path Enumeration of Permutations with k Occurrences of the Pattern 2-13</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.2.

%F 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.

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

%Y Column k=5 of A263776.

%K nonn

%O 1,6

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

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