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A209700 Triangle of coefficients of polynomials v(n,x) jointly generated with A209699; see the Formula section. 3

%I

%S 1,2,2,3,2,4,4,2,8,8,5,2,14,16,16,6,2,22,26,40,32,7,2,32,38,78,88,64,

%T 8,2,44,52,134,178,200,128,9,2,58,68,212,310,446,440,256,10,2,74,86,

%U 316,492,846,1042,968,512,11,2,92,106,450,732,1452,2062,2462

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209699; see the Formula section.

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

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

%F v(n,x)=2x*u(n-1,x)+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...2...4

%e 4...2...8....8

%e 5...2...14...16...16

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

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

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

%t v[n_, x_] := 2 x*u[n - 1, 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[%] (* A209699 *)

%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[%] (* A209700 *)

%Y Cf. A209699, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 12 2012

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Last modified November 14 04:56 EST 2019. Contains 329110 sequences. (Running on oeis4.)