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A210200 Triangle of coefficients of polynomials v(n,x) jointly generated with A210199; see the Formula section. 3

%I #5 Mar 30 2012 18:58:16

%S 1,2,2,4,5,2,7,12,7,2,12,25,21,9,2,20,50,53,32,11,2,33,96,124,94,45,

%T 13,2,54,180,273,250,150,60,15,2,88,331,577,617,445,223,77,17,2,143,

%U 600,1181,1444,1212,728,315,96,19,2,232,1075,2358,3242,3101,2163

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210199; see the Formula section.

%C Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...

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

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

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

%e 7....12...7....2

%e 12...25...21...9...2

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

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

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

%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[%] (* A210199 *)

%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[%] (* A210200 *)

%Y Cf. A210199, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 18 2012

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