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 A094218 #28 May 04 2025 01:57:45
%S A094218 0,0,0,2,25,198,1274,7280,38556,193800,937992,4412826,20309575,
%T A094218 91861770,409704750,1806342720,7887861960,34166674800,146977222320,
%U A094218 628521016500,2673950235138,11324837666604,47773836727540,200828153398752
%N A094218 Number of permutations of length n with exactly 2 occurrences of the pattern 2-13.
%D A094218 R. Lie, Permutations and Patterns, Master's Thesis, Goeteborg, Sweden: Chalmers University of Technology, 2004.
%H A094218 Alois P. Heinz, <a href="/A094218/b094218.txt">Table of n, a(n) for n = 1..500</a>
%H A094218 Robert 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 A094218 a(n) = n*binomial(2*n,n-4)/2.
%F A094218 From _Amiram Eldar_, May 04 2025: (Start)
%F A094218 Sum_{n>=4} 1/a(n) = 1147/45 - 34*Pi/(3*sqrt(3)) - 4*Pi^2/9.
%F A094218 Sum_{n>=4} (-1)^n/a(n) = 16*log(phi)^2 + 1588*log(phi)/(3*sqrt(5)) - 5272/45, where phi is the golden ratio (A001622). (End)
%t A094218 Table[n Binomial[2 n, n - 4]/2, {n, 30}] (* _Vincenzo Librandi_, Aug 20 2015 *)
%o A094218 (PARI) a(n)=n*binomial(2*n,n-4)/2
%o A094218 (Magma) [n*Binomial(2*n,n-4)/2: n in [1..30]]; // _Vincenzo Librandi_, Aug 20 2015
%Y A094218 Cf. A094219, A001622.
%Y A094218 Column k=2 of A263776.
%K A094218 nonn
%O A094218 1,4
%A A094218 _Benoit Cloitre_, May 27 2004