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 A133569 #19 Jan 25 2020 18:12:41 %S A133569 1,1,1,2,3,1,1,3,3,1,2,7,9,5,1,1,5,10,10,5,1,2,11,25,30,20,7,1,1,7,21, %T A133569 35,35,21,7,1,2,15,49,91,105,77,35,9,1,1,9,36,84,126,126,84,36,9,1 %N A133569 A133566 * A007318 as infinite lower triangular matrices. %C A133569 Row sums = A122756: (1, 2, 6, 8, 24, 32, 96, ...). %C A133569 With offset (0,4); triangle T(n,k), 0 <= k <= n, given by [1,1,-3,1,0,0,0,0,0,0,0,...] DELTA [1,0,-2,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Dec 15 2007 %F A133569 T(n,k) = T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-2), T(0,0) = 1, T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(2,2) = 1, T(n,k) = 0 if k < 0 or if k > n. - _Philippe Deléham_, Sep 17 2014 %F A133569 G.f.: (-1-x-x*y-x^2-x^2*y)/((x*y+1+x)*(-1+x+x*y)). - _R. J. Mathar_, Aug 12 2015 %e A133569 First few rows of the triangle: %e A133569 1; %e A133569 1, 1; %e A133569 2, 3, 1; %e A133569 1, 3, 3, 1; %e A133569 2, 7, 9, 5, 1; %e A133569 1, 5, 10, 10, 5, 1; %e A133569 2, 11, 25, 30, 20, 7, 1; %e A133569 1, 7, 21, 35, 35, 21, 7, 1; %e A133569 ... %Y A133569 Cf. A133566, A122756. %K A133569 nonn,tabl %O A133569 1,4 %A A133569 _Gary W. Adamson_, Sep 16 2007