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A210036 Triangle of coefficients of polynomials v(n,x) jointly generated with A210035; see the Formula section.

%I A210036 #4 Mar 30 2012 18:58:16
%S A210036 1,2,2,4,4,4,7,10,8,8,12,20,24,16,16,20,40,52,56,32,32,33,76,116,128,
%T A210036 128,64,64,54,142,240,312,304,288,128,128,88,260,488,688,800,704,640,
%U A210036 256,256,143,470,964,1496,1856,1984,1600,1408,512,512,232,840
%N A210036 Triangle of coefficients of polynomials v(n,x) jointly generated with A210035; see the Formula section.
%C A210036 For a discussion and guide to related arrays, see A208510.
%F A210036 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210036 v(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F A210036 where u(1,x)=1, v(1,x)=1.
%e A210036 First five rows:
%e A210036 1
%e A210036 2....2
%e A210036 4....4....4
%e A210036 7....10...8....8
%e A210036 12...20...24...16...16
%e A210036 First three polynomials v(n,x): 1, 2 + 2x , 4 + 4x + 4x^2.
%t A210036 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210036 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210036 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210036 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210036 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210036 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210036 TableForm[cu]
%t A210036 Flatten[%]    (* A210035 *)
%t A210036 Table[Expand[v[n, x]], {n, 1, z}]
%t A210036 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210036 TableForm[cv]
%t A210036 Flatten[%]    (* A210036 *)
%Y A210036 Cf. A210035, A208510.
%K A210036 nonn,tabl
%O A210036 1,2
%A A210036 _Clark Kimberling_, Mar 16 2012