A210230 - OEIS

%I #4 Mar 30 2012 18:58:16

%S 1,3,1,6,4,1,11,11,5,1,19,26,17,6,1,32,56,48,24,7,1,53,114,121,78,32,

%T 8,1,87,223,283,223,117,41,9,1,142,424,627,584,372,166,51,10,1,231,

%U 789,1334,1434,1073,579,226,62,11,1,375,1444,2750,3352,2879,1818

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210229; see the Formula section.

%C Alternating row sums: 1,2,3,4,5,6,... (A000027)

%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)=(x+1)*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 3....1

%e 6....4....1

%e 11...11...5....1

%e 19...26...17...6...1

%e First three polynomials v(n,x): 1, 3 + x , 6 + 4x + x^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_] := (x + 1)*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[%]     (* A210229 *)

%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[%]     (* A210230 *)

%Y Cf. A210229, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 20 2012