A209150 - OEIS

%I #5 Mar 30 2012 18:58:15

%S 1,2,1,4,4,1,7,10,5,1,11,21,17,7,1,16,40,46,28,8,1,22,71,107,87,39,10,

%T 1,29,119,224,232,144,55,11,1,37,190,434,555,443,226,70,13,1,46,291,

%U 792,1221,1198,773,328,91,14,1,56,430,1377,2511,2942,2318,1255

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208335; see the Formula section.

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

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

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

%F v(n,x)=x*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 2...1

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

%e 7...10....5....1

%e 11...21...17...7...1

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

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

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

%t v[n_, x_] := x*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[%]    (* A209150 *)

%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[%]    (* A208335 *)

%Y Cf. A208335, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 07 2012