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A208930 Triangle of coefficients of polynomials v(n,x) jointly generated with A208930; see the Formula section.

%I A208930 #6 Mar 30 2012 18:58:14
%S A208930 1,2,3,2,7,8,2,11,26,22,2,15,52,88,60,2,19,86,214,288,164,2,23,128,
%T A208930 416,820,916,448,2,27,178,710,1824,2984,2856,1224,2,31,236,1112,3500,
%U A208930 7464,10464,8768,3344,2,35,302,1638,6080,15884,29040,35664,26592
%N A208930 Triangle of coefficients of polynomials v(n,x) jointly generated with A208930; see the Formula section.
%C A208930 For a discussion and guide to related arrays, see A208510.
%F A208930 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208930 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A208930 where u(1,x)=1, v(1,x)=1.
%e A208930 First five rows:
%e A208930 1
%e A208930 2...3
%e A208930 2...7....8
%e A208930 2...11...26...22
%e A208930 2...15...52...88...60
%e A208930 First five polynomials v(n,x):
%e A208930 1
%e A208930 2 + 3x
%e A208930 2 + 7x + 8x^2
%e A208930 2 + 11x + 26x^2 + 22x^3
%e A208930 2 + 15x + 52x^2 + 88x^3 + 60x^4
%t A208930 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208930 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208930 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A208930 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208930 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208930 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208930 TableForm[cu]
%t A208930 Flatten[%]    (* A208909 *)
%t A208930 Table[Expand[v[n, x]], {n, 1, z}]
%t A208930 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208930 TableForm[cv]
%t A208930 Flatten[%]    (* A208930 *)
%Y A208930 Cf. A208909, A208510.
%K A208930 nonn,tabl
%O A208930 1,2
%A A208930 _Clark Kimberling_, Mar 04 2012