This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A120814 #8 Nov 14 2015 18:17:35 %S A120814 0,0,0,0,0,2,140,3262,47802,535990,5038418,41781432,315447990, %T A120814 2214289350,14664659100,92612930280,562220244768,3301016862024, %U A120814 18836205435208,104862661271840,571336322754792,3054404571541092,16056744308319000 %N A120814 Number of permutations of length n with exactly 6 occurrences of the pattern 2-13. %D A120814 R. Parviainen, Lattice path enumeration of permutations with k occurrences of the pattern 2-13, preprint, 2006. %D A120814 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 A120814 Alois P. Heinz, <a href="/A120814/b120814.txt">Table of n, a(n) for n = 1..500</a> %H A120814 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 A120814 a(n) = (20160 + 44448n + 548n^2 - 4196n^3 - 565n^4 + 67n^5 + 17n^6 + n^7)/(720(n+7)(n+6))binomial[2n, n-6]; generating function = x^6 C^13 (-42 + 4054C - 18354C^2 + 36038C^3 - 40660C^4 + 30080C^5 - 16090C^6 + 6914C^7 - 2604C^8 + 840C^9 - 202C^10 + 30C^11 - 2C^12)/(2-C)^11, where C=(1-Sqrt[1-4x])/(2x) is the Catalan function. %Y A120814 Cf. A002629, A094218, A094219, A120812-A120813, A120815-A120816. %Y A120814 Column k=6 of A263776. %K A120814 nonn %O A120814 1,6 %A A120814 Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 06 2006