A209152 - OEIS

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

%S 1,2,1,3,5,3,4,10,14,7,5,16,32,37,17,6,23,58,97,98,41,7,31,93,197,287,

%T 257,99,8,40,138,348,642,830,670,239,9,50,194,562,1234,2024,2360,1737,

%U 577,10,61,262,852,2148,4198,6220,6617,4482,1393,11,73,343

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208339; 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)+2x*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 3...5....3

%e 4...10...14...7

%e 5...16...32...37...17

%e First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 3x^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] + 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[%]    (* A209152 *)

%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[%]    (* A208339 *)

%Y Cf. A208339, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 07 2012