%I #10 Sep 08 2013 19:59:30

%S 1,2,3,4,4,10,8,5,18,28,16,6,28,64,72,32,7,40,120,200,176,64,8,54,200,

%T 440,576,416,128,9,70,308,840,1456,1568,960,256,10,88,448,1456,3136,

%U 4480,4096,2176,512,11,108,624,2352,6048,10752,13056,10368,4864

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A207628; see the Formula section.

%C Column n is divisible by 2^(n-1); row n ends with 2^(n-1).

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

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

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

%F The row sums =: 2, 7, 22, 67, ... are given by (5*3^n -1)/2 for n = 0, 1, 2, 3, ... . - _Philippe Deléham_, Feb 25 2012

%e First five rows:

%e 1

%e 2

%e 3...4

%e 4...10...8

%e 5...18...28...16

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

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

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

%t Table[Factor[u[n, x]], {n, 1, z}]

%t Table[Factor[v[n, x]], {n, 1, z}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%] (* A207625 *)

%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[%] (* A207626 *)

%Y Cf. A207628.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_, Feb 21 2012