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 A208923 Triangle of coefficients of polynomials u(n,x) jointly generated with A208908; see the Formula section. 3

%I

%S 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 296,214,64,1,26,134,408,738,808,490,128,1,30,184,678,1552,2286,2104,

%U 1110,256,1,34,242,1048,2906,5392,6674,5320,2474,512,1,38,308

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

%C For a discussion and guide to related arrays, see A208510.

%F u(n,x)=u(n-1,x)+2x*v(n-1,x),

%F v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,

%F where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 1...2

%e 1...6....4

%e 1...10...14...8

%e 1...14...32...38...16

%e First five polynomials u(n,x):

%e 1

%e 1 + 2x

%e 1 + 6x + 4x^2

%e 1 + 10x + 14x^2 + 8x^3

%e 1 + 14x + 32x^2 + 38x^3 + 16x^4

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];

%t v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;

%t Table[Expand[u[n, x]], {n, 1, z/2}]

%t Table[Expand[v[n, x]], {n, 1, z/2}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%] (* A208923 *)

%t Table[Expand[v[n, x]], {n, 1, z}]

%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

%t TableForm[cv]

%t Flatten[%] (* A208908 *)

%Y Cf. A208908, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 04 2012

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