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A208920 Triangle of coefficients of polynomials v(n,x) jointly generated with A208919; see the Formula section.

%I A208920 #6 Mar 30 2012 18:58:14
%S A208920 1,2,3,3,7,7,4,12,26,19,5,18,62,85,47,6,25,120,235,264,123,7,33,205,
%T A208920 515,879,803,311,8,42,322,980,2254,3038,2358,803,9,52,476,1694,4914,
%U A208920 8708,10156,6865,2047,10,63,672,2730,9576,20958,32640,32877,19588
%N A208920 Triangle of coefficients of polynomials v(n,x) jointly generated with A208919; see the Formula section.
%C A208920 For a discussion and guide to related arrays, see A208510.
%F A208920 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208920 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A208920 where u(1,x)=1, v(1,x)=1.
%e A208920 First five rows:
%e A208920 1
%e A208920 2...3
%e A208920 3...7....7
%e A208920 4...12...26...19
%e A208920 5...18...62...85...47
%e A208920 First five polynomials v(n,x):
%e A208920 1
%e A208920 2 + 3x
%e A208920 3 + 7x + 7x^2
%e A208920 4 + 12x + 26x^2 + 19x^3
%e A208920 5 + 18x + 62x^2 + 85x^3 + 47x^4
%t A208920 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208920 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208920 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A208920 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208920 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208920 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208920 TableForm[cu]
%t A208920 Flatten[%]    (* A208919 *)
%t A208920 Table[Expand[v[n, x]], {n, 1, z}]
%t A208920 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208920 TableForm[cv]
%t A208920 Flatten[%]    (* A208920 *)
%Y A208920 Cf. A208919, A208510.
%K A208920 nonn,tabl
%O A208920 1,2
%A A208920 _Clark Kimberling_, Mar 04 2012