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A208921 Triangle of coefficients of polynomials u(n,x) jointly generated with A208922; see the Formula section.

%I A208921 #7 Mar 30 2012 18:58:14
%S A208921 1,1,2,1,8,2,1,18,10,4,1,32,36,28,4,1,50,100,108,36,8,1,72,230,324,
%T A208921 196,80,8,1,98,462,840,772,440,104,16,1,128,840,1960,2456,1840,752,
%U A208921 208,16,1,162,1416,4200,6744,6464,3824,1488,272,32,1,200,2250,8376
%N A208921 Triangle of coefficients of polynomials u(n,x) jointly generated with A208922; see the Formula section.
%C A208921 For a discussion and guide to related arrays, see A208510.
%F A208921 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208921 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A208921 where u(1,x)=1, v(1,x)=1.
%e A208921 First five rows:
%e A208921 1
%e A208921 1...2
%e A208921 1...8....2
%e A208921 1...18...10...4
%e A208921 1...32...36...28...4
%e A208921 First five polynomials u(n,x):
%e A208921 1
%e A208921 1 + 2x
%e A208921 1 + 8x + 2x^2
%e A208921 1 + 18x + 10x^2 + 4x^3
%e A208921 1 + 32x + 36x^2 + 28x^3 + 4x^4
%t A208921 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208921 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208921 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A208921 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208921 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208921 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208921 TableForm[cu]
%t A208921 Flatten[%]    (* A208921 *)
%t A208921 Table[Expand[v[n, x]], {n, 1, z}]
%t A208921 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208921 TableForm[cv]
%t A208921 Flatten[%]    (* A208922 *)
%Y A208921 Cf. A208922, A208510.
%K A208921 nonn,tabl
%O A208921 1,3
%A A208921 _Clark Kimberling_, Mar 04 2012