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A210556 Triangle of coefficients of polynomials v(n,x) jointly generated with A210555; see the Formula section.

%I A210556 #5 Mar 30 2012 18:58:16
%S A210556 1,2,2,3,4,4,4,6,10,8,5,8,18,22,16,6,10,28,42,50,32,7,12,40,68,106,
%T A210556 110,64,8,14,54,100,188,250,242,128,9,16,70,138,300,468,594,526,256,
%U A210556 10,18,88,182,446,780,1188,1378,1138,512,11,20,108,232,630,1202
%N A210556 Triangle of coefficients of polynomials v(n,x) jointly generated with A210555; see the Formula section.
%C A210556 Alternating row sums: 1,0,3,0,9,0,27,0,81,0,...
%C A210556 For a discussion and guide to related arrays, see A208510.
%F A210556 u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A210556 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A210556 where u(1,x)=1, v(1,x)=1.
%e A210556 First five rows:
%e A210556 1
%e A210556 2...2
%e A210556 3...4...4
%e A210556 4...6...10...8
%e A210556 5...8...18...22...16
%e A210556 First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 4x^2.
%t A210556 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210556 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210556 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210556 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210556 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210556 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210556 TableForm[cu]
%t A210556 Flatten[%]   (* A210555 *)
%t A210556 Table[Expand[v[n, x]], {n, 1, z}]
%t A210556 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210556 TableForm[cv]
%t A210556 Flatten[%]   (* A210556 *)
%Y A210556 Cf. A210555, A208510.
%K A210556 nonn,tabl
%O A210556 1,2
%A A210556 _Clark Kimberling_, Mar 22 2012