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A209163 Triangle of coefficients of polynomials v(n,x) jointly generated with A209162; see the Formula section. 3

%I

%S 1,2,3,3,9,5,4,20,26,11,5,38,82,71,21,6,65,204,279,176,43,7,103,439,

%T 849,845,425,85,8,154,854,2192,3050,2386,990,171,9,220,1540,5034,9174,

%U 9940,6396,2267,341,10,303,2616,10578,24232,34102,30228,16521

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209162; see the Formula section.

%C Alternating row sums: 1,-1,-1,-1,-,1-,1-,1,-1,...

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

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

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

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

%e First five rows:

%e 1

%e 2...3

%e 3...9...5

%e 4...20...26...11

%e 5...38...82...71...21

%e First three polynomials v(n,x): 1, 2 + 3x, 3 + 9x + 5x^2.

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

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

%t v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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[%] (* A209162 *)

%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[%] (* A209163 *)

%Y Cf. A209162, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 07 2012

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Last modified November 20 10:09 EST 2019. Contains 329334 sequences. (Running on oeis4.)