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A209154 Triangle of coefficients of polynomials u(n,x) jointly generated with A209157; see the Formula section. 3

%I

%S 1,2,1,4,5,2,7,14,10,2,11,32,36,18,4,16,65,104,82,32,4,22,121,258,282,

%T 168,52,8,29,210,574,820,676,328,88,8,37,344,1176,2116,2264,1504,608,

%U 136,16,46,537,2256,4980,6640,5672,3136,1096,224,16,56,805

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209157; see the Formula section.

%C Last number in each row is a power of 2.

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

%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)+v(n-1,x)+1,

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

%e First five rows:

%e 1

%e 2....1

%e 4....5....2

%e 7....14...10...2

%e 11...32...36...18...4

%e First three polynomials v(n,x): 1, 2 + x, 4 + 5x + 2x^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] + 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[%] (* A209154 *)

%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[%] (* A209157 *)

%Y Cf. A209157, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 07 2012

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)