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%I #6 Nov 14 2015 18:20:01
%S 1,44,700,7460,63648,470934,3155691,19660630,115855025,653392740,
%T 3556757490,18805317960,97034823600,490465092600,2435567286708,
%U 11910569958216,57470522059594,274051266477560,1293219035408080
%N Number of permutations of length n with exactly 4 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="/A120812/b120812.txt">Table of n, a(n) for n = 5..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) = (-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.
%Y Cf. A002629, A094218, A094219, A120813-A120816.
%Y Column k=4 of A263776.
%K nonn
%O 5,2
%A Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 05 2006
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