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Triangle of coefficients of polynomials v(n,x) jointly generated with A210211; see the Formula section.
3

%I #4 Mar 30 2012 18:58:16

%S 1,2,2,3,5,4,4,10,11,8,5,16,28,23,16,6,24,51,72,47,32,7,33,90,144,176,

%T 95,64,8,44,138,294,377,416,191,128,9,56,208,492,878,938,960,383,256,

%U 10,70,290,830,1577,2462,2251,2176,767,512,11,85,400,1250,2952

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210211; see the Formula section.

%C First and last terms of row n: n and 2^(n-1)

%C Alternating row sums are signed products of two Fibonacci numbers.

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

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

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

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

%e First five rows:

%e 1

%e 2...2

%e 3...5...4

%e 4...10...11...8

%e 5...16...28...23...16

%e First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 4x^2.

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

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

%t v[n_, x_] := u[n - 1, x] + 2 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[%] (* A210211 *)

%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[%] (* A210212 *)

%Y Cf. A210211, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 19 2012