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A208907 Triangle of coefficients of polynomials u(n,x) jointly generated with A208756; see the Formula section.

%I A208907 #5 Mar 30 2012 18:58:14
%S A208907 1,1,2,1,4,4,1,6,8,8,1,8,12,20,16,1,10,16,36,44,32,1,12,20,56,84,100,
%T A208907 64,1,14,24,80,136,212,220,128,1,16,28,108,200,376,500,484,256,1,18,
%U A208907 32,140,276,600,936,1188,1052,512,1,20,36,176,364,892,1560
%N A208907 Triangle of coefficients of polynomials u(n,x) jointly generated with A208756; see the Formula section.
%C A208907 For a discussion and guide to related arrays, see A208510.
%F A208907 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208907 v(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A208907 where u(1,x)=1, v(1,x)=1.
%e A208907 First five rows:
%e A208907 1
%e A208907 1...2
%e A208907 1...4...4
%e A208907 1...6...8....8
%e A208907 1...8...12...20...16
%e A208907 First five polynomials u(n,x):
%e A208907 1
%e A208907 1 + 2x
%e A208907 1 + 4x + 4x^2
%e A208907 1 + 6x + 8x^2 + 8x^3
%e A208907 1 + 8x + 12x^2 + 20x^3 + 16x^4
%t A208907 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208907 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208907 v[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A208907 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208907 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208907 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208907 TableForm[cu]
%t A208907 Flatten[%]    (* A208907 *)
%t A208907 Table[Expand[v[n, x]], {n, 1, z}]
%t A208907 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208907 TableForm[cv]
%t A208907 Flatten[%]    (* A208756 *)
%Y A208907 Cf. A208756, A208510.
%K A208907 nonn,tabl
%O A208907 1,3
%A A208907 _Clark Kimberling_, Mar 03 2012