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 A120812 #6 Nov 14 2015 18:20:01 %S A120812 1,44,700,7460,63648,470934,3155691,19660630,115855025,653392740, %T A120812 3556757490,18805317960,97034823600,490465092600,2435567286708, %U A120812 11910569958216,57470522059594,274051266477560,1293219035408080 %N A120812 Number of permutations of length n with exactly 4 occurrences of the pattern 2-13. %D A120812 R. Parviainen, Lattice path enumeration of permutations with k occurrences of the pattern 2-13, preprint, 2006. %D A120812 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 A120812 Alois P. Heinz, <a href="/A120812/b120812.txt">Table of n, a(n) for n = 5..500</a> %H A120812 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 A120812 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 A120812 Cf. A002629, A094218, A094219, A120813-A120816. %Y A120812 Column k=4 of A263776. %K A120812 nonn %O A120812 5,2 %A A120812 Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 05 2006