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A209762 Triangle of coefficients of polynomials v(n,x) jointly generated with A209761; see the Formula section.

%I A209762 #8 Apr 15 2012 03:45:24
%S A209762 1,2,2,3,5,4,4,10,14,8,5,17,34,36,16,6,26,68,104,88,32,7,37,120,240,
%T A209762 296,208,64,8,50,194,480,776,800,480,128,9,65,294,868,1736,2352,2080,
%U A209762 1088,256,10,82,424,1456,3472,5824,6784,5248,2432,512,11,101,588
%N A209762 Triangle of coefficients of polynomials v(n,x) jointly generated with A209761; see the Formula section.
%C A209762 Column 1: 1,2,3,4,5,6,7,8,...
%C A209762 Column 2: 1+1, 1+2^2, 1+3^2, 1+4^2,...
%C A209762 Last term in row n:  2^(n-1)
%C A209762 Alternating row sums: 1,0,2,0,2,0,2,0,2,0,2,0,...
%C A209762 For a discussion and guide to related arrays, see A208510.
%F A209762 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209762 v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209762 where u(1,x)=1, v(1,x)=1.
%e A209762 First five rows:
%e A209762 1
%e A209762 2...2
%e A209762 3...5....4
%e A209762 4...10...14...8
%e A209762 5...17...34...36...16
%e A209762 First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 4x^2.
%t A209762 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209762 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209762 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209762 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209762 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209762 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209762 TableForm[cu]
%t A209762 Flatten[%]    (* A209761 *)
%t A209762 Table[Expand[v[n, x]], {n, 1, z}]
%t A209762 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209762 TableForm[cv]
%t A209762 Flatten[%]    (* A209762 *)
%Y A209762 Cf. A209761, A208510.
%K A209762 nonn,tabl
%O A209762 1,2
%A A209762 _Clark Kimberling_, Mar 14 2012