A210226 - OEIS

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

%S 1,2,3,3,9,5,4,18,24,7,5,30,66,51,9,6,45,140,189,94,11,7,63,255,505,

%T 457,157,13,8,84,420,1110,1516,976,244,15,9,108,644,2142,3986,3960,

%U 1896,359,17,10,135,936,3766,8960,12338,9276,3419,506,19,11,165

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210225; see the Formula section.

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

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

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

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

%e First five rows:

%e 1

%e 2...3

%e 3...9....5

%e 4...18...24...7

%e 5...30...66...51...9

%e First three polynomials v(n,x): 1, 2 + 3x , 3 + 9x + 5x^2.

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

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

%t v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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[%]     (* A210225 *)

%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[%]     (* A210226 *)

%Y Cf. A210225, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 20 2012