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A210218 Triangle of coefficients of polynomials v(n,x) jointly generated with A210217; see the Formula section. 3

%I

%S 1,1,3,1,4,7,1,4,13,15,1,4,14,38,31,1,4,14,47,103,63,1,4,14,48,151,

%T 264,127,1,4,14,48,163,462,649,255,1,4,14,48,164,544,1348,1546,511,1,

%U 4,14,48,164,559,1768,3769,3595,1023,1,4,14,48,164,560,1893,5564

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210217; see the Formula section.

%C Limiting row: A007070

%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)=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 1...3

%e 1...4...7

%e 1...4...13...15

%e 1...4...14...38...31

%e First three polynomials v(n,x): 1, 1 + 3x , 1 + 4x + 7x^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_] := 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[%] (* A210217 *)

%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[%] (* A210218 *)

%Y Cf. A210217, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 19 2012

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Last modified January 20 07:59 EST 2020. Contains 331081 sequences. (Running on oeis4.)