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A208923 Triangle of coefficients of polynomials u(n,x) jointly generated with A208908; see the Formula section.

%I A208923 #5 Mar 30 2012 18:58:14
%S A208923 1,1,2,1,6,4,1,10,14,8,1,14,32,38,16,1,18,58,104,90,32,1,22,92,222,
%T A208923 296,214,64,1,26,134,408,738,808,490,128,1,30,184,678,1552,2286,2104,
%U A208923 1110,256,1,34,242,1048,2906,5392,6674,5320,2474,512,1,38,308
%N A208923 Triangle of coefficients of polynomials u(n,x) jointly generated with A208908; see the Formula section.
%C A208923 For a discussion and guide to related arrays, see A208510.
%F A208923 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208923 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A208923 where u(1,x)=1, v(1,x)=1.
%e A208923 First five rows:
%e A208923 1
%e A208923 1...2
%e A208923 1...6....4
%e A208923 1...10...14...8
%e A208923 1...14...32...38...16
%e A208923 First five polynomials u(n,x):
%e A208923 1
%e A208923 1 + 2x
%e A208923 1 + 6x + 4x^2
%e A208923 1 + 10x + 14x^2 + 8x^3
%e A208923 1 + 14x + 32x^2 + 38x^3 + 16x^4
%t A208923 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208923 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208923 v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A208923 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208923 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208923 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208923 TableForm[cu]
%t A208923 Flatten[%]    (* A208923 *)
%t A208923 Table[Expand[v[n, x]], {n, 1, z}]
%t A208923 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208923 TableForm[cv]
%t A208923 Flatten[%]    (* A208908 *)
%Y A208923 Cf. A208908, A208510.
%K A208923 nonn,tabl
%O A208923 1,3
%A A208923 _Clark Kimberling_, Mar 04 2012