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 A133087 #14 Mar 07 2022 02:06:38
%S A133087 1,2,1,1,2,1,2,5,4,1,1,4,6,4,1,2,9,16,14,6,1,1,6,15,20,15,6,1,2,13,36,
%T A133087 55,50,27,8,1,1,8,28,56,70,56,28,8,1,2,17,64,140,196,182,112,44,10,1
%N A133087 A133080 * A007318.
%C A133087 Row sums = A084221: (1, 3, 4, 12, 16, 48, 64, 192, ...).
%C A133087 Subtriangle of (0, 2, -3/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Mar 03 2012
%H A133087 G. C. Greubel, <a href="/A133087/b133087.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A133087 A133080 * A007318 as infinite lower triangular matrices.
%F A133087 G.f.: (1+2*x+y*x)/(1-(1+y)^2*x^2). - _Philippe Deléham_, Mar 03 2012
%F A133087 T(n,k) = T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-1), T(0,0) = 1, T(1,0) = 2, T(1,1) = 1. - _Philippe Deléham_, Mar 03 2012
%F A133087 Sum_{k=0..n} T(n,k)*x^k = A059841(n), A019590(n+1), A000034(n), A084221(n), A133125(n) for x = -2, -1, 0, 1, 2 respectively. - _Philippe Deléham_, Mar 03 2012
%e A133087 First few rows of the triangle:
%e A133087 1;
%e A133087 2, 1;
%e A133087 1, 2, 1;
%e A133087 2, 5, 4, 1;
%e A133087 1, 4, 6, 4, 1;
%e A133087 2, 9, 16, 14, 6, 1;
%e A133087 1, 6, 15, 20, 15, 6, 1;
%e A133087 2, 13, 36, 55, 50, 27, 8, 1;
%e A133087 1, 8, 28, 56, 70, 56, 28, 8, 1;
%e A133087 ...
%e A133087 Triangle (0, 2, -3/2, -1/2, 0, 0, 0, ...) DELTA (1, 0, -1, 0, 0, 0, ...) begins:
%e A133087 1;
%e A133087 0, 1;
%e A133087 0, 2, 1;
%e A133087 0, 1, 2, 1;
%e A133087 0, 2, 5, 4, 1;
%e A133087 0, 1, 4, 6, 4, 1;
%e A133087 0, 2, 9, 16, 14, 6, 1;
%e A133087 0, 1, 6, 15, 20, 15, 6, 1;
%e A133087 0, 2, 13, 36, 55, 50, 27, 8, 1;
%e A133087 0, 1, 8, 28, 56, 70, 56, 28, 8, 1;
%e A133087 ...
%t A133087 CoefficientList[CoefficientList[Series[(1 + 2*x + y*x)/(1 - (1 + y)^2*x^2), {x, 0, 10}, {y, 0, 10}], x], y] // Flatten (* _G. C. Greubel_, Oct 21 2017 *)
%Y A133087 Cf. A133080, A084221.
%Y A133087 Columns: A000007, A114752, A133092.
%K A133087 nonn,tabl
%O A133087 0,2
%A A133087 _Gary W. Adamson_, Sep 08 2007