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 A208609 Triangle of coefficients of polynomials v(n,x) jointly generated with A208608; see the Formula section. 3

%I

%S 1,2,2,2,4,3,2,6,9,5,2,8,17,18,8,2,10,27,41,35,13,2,12,39,76,93,66,21,

%T 2,14,53,125,196,200,122,34,2,16,69,190,360,472,415,222,55,2,18,87,

%U 273,603,957,1083,837,399,89,2,20,107,376,945,1750,2400,2392

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208608; see the Formula section.

%C v(n,n)=Fibonacci(n+1)=A000045(n+1).

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

%F v(n,x)=(x+1)*u(n-1,x)+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 2...4...3

%e 2...6...9....5

%e 2...8...17...18...8

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

%e 1

%e 2 + 2x

%e 2 + 4x + 3x^2

%e 2 + 6x + 9x^2 + 5x^3

%e 2 + 8x + 17x^2 + 18x^3 + 8x^4

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

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

%t v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A208608 *)

%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[%] (* A208609 *)

%Y Cf. A208608.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Feb 29 2012

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Last modified August 1 09:25 EDT 2021. Contains 346385 sequences. (Running on oeis4.)