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 A208906 Triangle of coefficients of polynomials v(n,x) jointly generated with A208905; see the Formula section. 3

%I #5 Mar 30 2012 18:58:14

%S 1,2,1,3,2,2,4,3,8,2,5,4,20,8,4,6,5,40,20,24,4,7,6,70,40,84,24,8,8,7,

%T 112,70,224,84,64,8,9,8,168,112,504,224,288,64,16,10,9,240,168,1008,

%U 504,960,288,160,16,11,10,330,240,1848,1008,2640,960,880,160,32

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208905; see the Formula section.

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

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

%F v(n,x)=x*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 3...2...2

%e 4...3...8....2

%e 5...4...20...8...4

%e First five polynomials v(n,x):

%e 1

%e 2 + x

%e 3 + 2x + 2x^2

%e 4 + 3x + 8x^2 + 2x^3

%e 5 + 4x + 20x^2 + 8x^3 + 4x^4

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

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

%t v[n_, x_] := 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[%] (* A208905 *)

%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[%] (* A208906 *)

%Y Cf. A208905, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 03 2012

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Last modified August 7 06:05 EDT 2024. Contains 375008 sequences. (Running on oeis4.)