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 A208910 #16 Jan 26 2020 01:08:22
%S A208910 1,1,3,1,3,8,1,3,10,22,1,3,12,32,60,1,3,14,42,100,164,1,3,16,52,144,
%T A208910 308,448,1,3,18,62,192,480,936,1224,1,3,20,72,244,680,1568,2816,3344,
%U A208910 1,3,22,82,300,908,2352,5040,8400,9136,1,3,24,92,360,1164,3296
%N A208910 Triangle of coefficients of polynomials v(n,x) jointly generated with A208755; see the Formula section.
%C A208910 For a discussion and guide to related arrays, see A208510.
%C A208910 Subtriangle of the triangle given by (1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 3, -1/3, -2/3, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Apr 01 2012
%F A208910 u(n,x) = u(n-1,x) + 2x*v(n-1,x),
%F A208910 v(n,x) = x*u(n-1,x) + 2x*v(n-1,x)+1,
%F A208910 where u(1,x)=1, v(1,x)=1.
%F A208910 From _Philippe Deléham_, Apr 01 2012: (Start)
%F A208910 As DELTA-triangle T(n,k) with 0 <= k <= n:
%F A208910 G.f.: (1 - 2*y*x + 3*y*x^2 - 2*y^2*x^2)/(1 - x - 2*y*x + 2*y*x^2 - 2*y^2*x^2).
%F A208910 T(n,k) = T(n-1,k) + 2*T(n-1,k-1) - 2*T(n-2,k-1) + 2*T(n-2,k-2), T(0,0) = T(1,0) = T(2,0) = 1, T(2,1) = 3, T(1,1) = T(2,2) = 0 and T(n,k) = 0 if k < 0 or if k > n. (End)
%F A208910 T(n,k) = 2*A208757(n,k) - A208332(n,k). - _Philippe Deléham_, Apr 15 2012
%e A208910 First five rows:
%e A208910 1;
%e A208910 1, 3;
%e A208910 1, 3, 8;
%e A208910 1, 3, 10, 22;
%e A208910 1, 3, 12, 32, 60;
%e A208910 First five polynomials v(n,x):
%e A208910 1
%e A208910 1 + 3x
%e A208910 1 + 3x + 8x^2
%e A208910 1 + 3x + 10x^2 + 22x^3
%e A208910 1 + 3x + 12x^2 + 32x^3 + 60x^4
%e A208910 From _Philippe Deléham_, Apr 01 2012: (Start)
%e A208910 (1, 0, -1, 1, 0, 0, ...) DELTA (0, 3, -1/3, -2/3, 0, 0, ...) begins:
%e A208910 1;
%e A208910 1, 0;
%e A208910 1, 3, 0;
%e A208910 1, 3, 8, 0;
%e A208910 1, 3, 10, 22, 0;
%e A208910 1, 3, 12, 32, 60, 0;
%e A208910 1, 3, 14, 42, 100, 164, 0; (End)
%t A208910 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208910 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208910 v[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A208910 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208910 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208910 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208910 TableForm[cu]
%t A208910 Flatten[%] (* A208755 *)
%t A208910 Table[Expand[v[n, x]], {n, 1, z}]
%t A208910 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208910 TableForm[cv]
%t A208910 Flatten[%] (* A208910 *)
%Y A208910 Cf. A208755, A208510.
%K A208910 nonn,tabl
%O A208910 1,3
%A A208910 _Clark Kimberling_, Mar 03 2012