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%I #9 Nov 14 2015 18:16:17
%S 42,1664,33338,468200,5253864,50442128,431645370,3380738400,
%T 24682378500,170201240352,1119398566704,7074531999584,43215257135312,
%U 256343213520000,1482127305153560,8378542979807616,46428426576857886
%N Number of permutations of length n with exactly 7 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="/A120815/b120815.txt">Table of n, a(n) for n = 7..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+5)(40320 + 67824n - 20180n^2 - 7556n^3 - 5n^4 + 211n^5 + 25n^6 + n^7)/(5040(n+8)(n+9))Binomial[2n, n-7]; generating function = x^7 C^15(32 + 16516C - 92666C^2 + 215944C^3 - 281094C^4 + 225628C^5 - 110922C^6 + 25360C^7 + 7066C^8 - 9364C^9 + 4622C^10 - 1440C^11 + 294C^12 - 36C^13 + 2C^14)/(2-C)^13, where C=(1-Sqrt[1-4x])/(2x) is the Catalan function.
%Y Cf. A002629, A094218, A094219, A120812-A120814, A120816.
%Y Column k=7 of A263776.
%K nonn
%O 7,1
%A Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 06 2006; definition corrected Feb 08 2008
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