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A208914 Triangle of coefficients of polynomials v(n,x) jointly generated with A208913; see the Formula section.

%I A208914 #5 Mar 30 2012 18:58:14
%S A208914 1,2,2,3,4,4,4,6,16,8,5,8,40,32,16,6,10,80,80,96,32,7,12,140,160,336,
%T A208914 192,64,8,14,224,280,896,672,512,128,9,16,336,448,2016,1792,2304,1024,
%U A208914 256,10,18,480,672,4032,4032,7680,4608,2560,512,11,20,660,960
%N A208914 Triangle of coefficients of polynomials v(n,x) jointly generated with A208913; see the Formula section.
%C A208914 For a discussion and guide to related arrays, see A208510.
%F A208914 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208914 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A208914 where u(1,x)=1, v(1,x)=1.
%e A208914 First five rows:
%e A208914 1
%e A208914 2...2
%e A208914 3...4...4
%e A208914 4...6...16...8
%e A208914 5...8...40...32...16
%e A208914 First five polynomials v(n,x):
%e A208914 1
%e A208914 2 + 2x
%e A208914 3 + 4x + 4x^2
%e A208914 4 + 6x + 16x^2 + 8x^3
%e A208914 5 + 8x + 40x^2 + 32x^3 + 16x^4
%t A208914 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208914 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208914 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A208914 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208914 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208914 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208914 TableForm[cu]
%t A208914 Flatten[%]    (* A208913 *)
%t A208914 Table[Expand[v[n, x]], {n, 1, z}]
%t A208914 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208914 TableForm[cv]
%t A208914 Flatten[%]    (* A208914 *)
%Y A208914 Cf. A208913, A208510.
%K A208914 nonn,tabl
%O A208914 1,2
%A A208914 _Clark Kimberling_, Mar 03 2012