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A208527 Triangle of coefficients of polynomials v(n,x) jointly generated with A208526; see the Formula section.

%I A208527 #5 Mar 30 2012 18:58:13
%S A208527 1,1,4,1,4,10,1,4,12,28,1,4,14,40,76,1,4,16,52,124,208,1,4,18,64,176,
%T A208527 384,568,1,4,20,76,232,592,1168,1552,1,4,22,88,292,832,1936,3520,4240,
%U A208527 1,4,24,100,356,1104,2880,6240,10512,11584,1,4,26,112,424,1408
%N A208527 Triangle of coefficients of polynomials v(n,x) jointly generated with A208526; see the Formula section.
%F A208527 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208527 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A208527 where u(1,x)=1, v(1,x)=1.
%e A208527 First five rows:
%e A208527 1
%e A208527 1...4
%e A208527 1...4...10
%e A208527 1...4...12...28
%e A208527 1...4...14...40...76
%e A208527 First five polynomials v(n,x):
%e A208527 1
%e A208527 1 + 4x
%e A208527 1 + 4x + 10x^2
%e A208527 1 + 4x + 12x^2 + 28x^3
%e A208527 1 + 4x + 14x^2 + 40x^3 + 76x^4
%t A208527 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208527 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208527 v[n_, x_] := 2 x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A208527 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208527 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208527 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208527 TableForm[cu]
%t A208527 Flatten[%]  (* A208526 *)
%t A208527 Table[Expand[v[n, x]], {n, 1, z}]
%t A208527 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208527 TableForm[cv]
%t A208527 Flatten[%]  (* A208527 *)
%Y A208527 Cf. A208526.
%K A208527 nonn,tabl
%O A208527 1,3
%A A208527 _Clark Kimberling_, Feb 29 2012