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A209751 Triangle of coefficients of polynomials u(n,x) jointly generated with A209752; see the Formula section. 3

%I #6 Mar 30 2012 18:58:15

%S 1,1,2,2,5,4,2,10,15,8,3,14,35,39,16,3,22,63,108,95,32,4,27,109,235,

%T 309,223,64,4,38,160,454,782,838,511,128,5,44,242,770,1688,2408,2183,

%U 1151,256,5,58,322,1264,3226,5776,7009,5512,2559,512,6,65,450

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A209752; 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)=x*u(n-1,x)+(x+1)*v(n-1,x),

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

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

%e First five rows:

%e 1

%e 1...2

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

%e 2...10...15...8

%e 3...14...35...39...16

%e First three polynomials u(n,x): 1, 1 + 2x, 2 + 5x + 4x^2.

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

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

%t v[n_, x_] := u[n - 1, x] + 2 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[%] (* A209751 *)

%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[%] (* A209752 *)

%Y Cf. A209752, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 14 2012

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Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)