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

%I A209761 #7 Mar 30 2012 18:58:15
%S A209761 1,1,2,2,5,4,3,10,14,8,4,17,34,36,16,5,26,68,104,88,32,6,37,120,240,
%T A209761 296,208,64,7,50,194,480,776,800,480,128,8,65,294,868,1736,2352,2080,
%U A209761 1088,256,9,82,424,1456,3472,5824,6784,5248,2432,512,10,101,588
%N A209761 Triangle of coefficients of polynomials u(n,x) jointly generated with A209762; see the Formula section.
%C A209761 Column 1: 1,1,2,3,4,5,6,7,...
%C A209761 Column 2: 1+1, 1+2^2, 1+3^2, 1+4^2,...
%C A209761 Last term in row n:  2^(n-1)
%C A209761 Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...; A033999
%C A209761 For a discussion and guide to related arrays, see A208510.
%F A209761 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209761 v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209761 where u(1,x)=1, v(1,x)=1.
%e A209761 First five rows:
%e A209761 1
%e A209761 1...2
%e A209761 2...5....4
%e A209761 3...10...14...8
%e A209761 4...17...34...36...16
%e A209761 First three polynomials u(n,x): 1, 1 + 2x, 2 + 5x + 4x^2.
%t A209761 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209761 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209761 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209761 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209761 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209761 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209761 TableForm[cu]
%t A209761 Flatten[%]    (* A209761 *)
%t A209761 Table[Expand[v[n, x]], {n, 1, z}]
%t A209761 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209761 TableForm[cv]
%t A209761 Flatten[%]    (* A209762 *)
%Y A209761 Cf. A209762, A208510.
%K A209761 nonn,tabl
%O A209761 1,3
%A A209761 _Clark Kimberling_, Mar 14 2012