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 A160232 #23 Jan 27 2020 01:46:47
%S A160232 1,1,1,1,2,2,1,3,5,4,1,4,9,12,8,1,5,14,25,28,16,1,6,20,44,66,64,32,1,
%T A160232 7,27,70,129,168,144,64,1,8,35,104,225,360,416,320,128,1,9,44,147,363,
%U A160232 681,968,1008,704,256,1,10,54,200,553,1182,1970,2528,2400,1536,512,1,11,65
%N A160232 Array read by antidiagonals: row n has g.f. ((1-x)/(1-2x))^n.
%C A160232 Suggested by a question from Phyllis Chinn (Humboldt State University).
%C A160232 As triangle, mirror image of A105306. - _Philippe Deléham_, Nov 01 2011
%C A160232 A160232 is jointly generated with A208341 as a triangular array of coefficients of polynomials u(n,x): initially, u(1,x)=v(1,x)=1; for n > 1, u(n,x) = u(n-1,x) + x*v(n-1)x and v(n,x) = u(n-1,x) + 2x*v(n-1,x). See the Mathematica section. - _Clark Kimberling_, Feb 25 2012
%C A160232 Subtriangle of the triangle T(n,k) given by (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Mar 08 2012
%F A160232 From _Philippe Deléham_, Mar 08 2012: (Start)
%F A160232 As DELTA-triangle T(n,k) with 0 <= k <= n:
%F A160232 T(n,k) = T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k-1), T(0,0) = 1, T(1,0) = 1, T(1,1) = 0, T(n,k) = 0 if k < 0 or if k > n.
%F A160232 G.f.: (1-2*y*x)/(1-2*y*x-x+y*x^2).
%F A160232 Sum_{k=0..n, n>0} T(n,k)*x^k = A000012(n), A001519(n), A052984(n-1) for x = 0, 1, 2 respectively. (End)
%e A160232 Array begins:
%e A160232 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, ...
%e A160232 1, 2, 5, 12, 28, 64, 144, 320, 704, 1536, 3328, 7168, 15360, 32768, 69632, 147456, 311296, 655360, 1376256, ...
%e A160232 1, 3, 9, 25, 66, 168, 416, 1008, 2400, 5632, 13056, 29952, 68096, 153600, 344064, 765952, 1695744, 3735552, ...
%e A160232 1, 4, 14, 44, 129, 360, 968, 2528, 6448, 16128, 39680, 96256, 230656, 546816, 1284096, 2990080, 6909952, ...
%e A160232 1, 5, 20, 70, 225, 681, 1970, 5500, 14920, 39520, 102592, 261760, 657920, 1632000, 4001280, 9708544, ...
%e A160232 1, 6, 27, 104, 363, 1182, 3653, 10836, 31092, 86784, 236640, 632448, 1661056, 4296192, 10961664, 27630592, ...
%e A160232 From _Clark Kimberling_, Feb 25 2012: (Start)
%e A160232 As a triangle (see Comments):
%e A160232 1;
%e A160232 1, 1;
%e A160232 1, 2, 2;
%e A160232 1, 3, 5, 4;
%e A160232 1, 4, 9, 12, 8; (End)
%e A160232 From _Philippe Deléham_, Mar 08 2012: (Start)
%e A160232 (1, 0, 0, 0, 0, ...) DELTA (0, 1, 1, 0, 0, 0, ...) begins:
%e A160232 1;
%e A160232 1, 0;
%e A160232 1, 1, 0;
%e A160232 1, 2, 2, 0;
%e A160232 1, 3, 5, 4, 0;
%e A160232 1, 4, 9, 12, 8, 0;
%e A160232 1, 5, 14, 25, 28, 16, 0; (End)
%t A160232 u[1, x_] := 1; v[1, x_] := 1; z = 13;
%t A160232 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A160232 v[n_, x_] := u[n - 1, x] + 2*x*v[n - 1, x];
%t A160232 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A160232 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A160232 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A160232 TableForm[cu]
%t A160232 Flatten[%] (* A160232 *)
%t A160232 Table[Expand[v[n, x]], {n, 1, z}]
%t A160232 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A160232 TableForm[cv]
%t A160232 Flatten[%] (* A208341 *)
%t A160232 (* _Clark Kimberling_, Feb 25 2012 *)
%Y A160232 Rows give A011782, A045623, A058396, A062109, A169792-A169797.
%Y A160232 Cf. A062110, A105306, A208341.
%K A160232 nonn,tabl
%O A160232 1,5
%A A160232 _N. J. A. Sloane_, May 15 2010