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 A120815 #15 Sep 15 2024 01:37:05 %S A120815 42,1664,33338,468200,5253864,50442128,431645370,3380738400, %T A120815 24682378500,170201240352,1119398566704,7074531999584,43215257135312, %U A120815 256343213520000,1482127305153560,8378542979807616,46428426576857886 %N A120815 Number of permutations of length n with exactly 7 occurrences of the pattern 2-13. %D A120815 R. Parviainen, Lattice path enumeration of permutations with k occurrences of the pattern 2-13, preprint, 2006. %D A120815 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 A120815 Alois P. Heinz, <a href="/A120815/b120815.txt">Table of n, a(n) for n = 7..500</a> %H A120815 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 A120815 a(n) = (n+5)*(40320 + 67824*n - 20180*n^2 - 7556*n^3 - 5*n^4 + 211*n^5 + 25*n^6 + n^7)*binomial(2*n, n-7)/(5040*(n+8)*(n+9)). %F A120815 G.f.: x^7*C^15*(132 + 16516*C - 92666*C^2 + 215944*C^3 - 281094*C^4 + 225628*C^5 - 110922*C^6 + 25360*C^7 + 7066*C^8 - 9364*C^9 + 4622*C^10 - 1440*C^11 + 294*C^12 - 36*C^13 + 2*C^14)/(2-C)^13, where C=(1-sqrt(1-4*x))/(2*x) is the Catalan function. %Y A120815 Cf. A002629, A094218, A094219, A120812-A120814, A120816. %Y A120815 Column k=7 of A263776. %K A120815 nonn,easy %O A120815 7,1 %A A120815 Robert Parviainen (robertp(AT)ms.unimelb.edu.au), Jul 06 2006; definition corrected Feb 08 2008