A193902 - OEIS

%I #6 Mar 30 2012 18:57:39

%S 1,2,1,4,6,3,8,12,14,7,16,24,28,30,15,32,48,56,60,62,31,64,96,112,120,

%T 124,126,63,128,192,224,240,248,252,254,127,256,384,448,480,496,504,

%U 508,510,255,512,768,896,960,992,1008,1016,1020,1022,511,1024,1536,1792,1920,1984,2016,2032,2040,2044,2046,1023,2048,3072,3584,3840

%N Triangular array:  the self-fusion of (p(n,x)), where p(n,x)=2x*p(n-1,x)+1, p(0,x)=1.

%C See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.

%e First six rows of A193902:

%e 1

%e 2....1

%e 4....6....3

%e 8....12...14...7

%e 16...24...28...30...15

%e 32...48...56...60...62...31

%t z = 12;

%t p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 1;

%t q[n_, x_] := 2 x*q[n - 1, x] + 1; q[0, x_] := 1;

%t t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;

%t w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1

%t g[n_] := CoefficientList[w[n, x], {x}]

%t TableForm[Table[Reverse[g[n]], {n, -1, z}]]

%t Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193902 *)

%t TableForm[Table[g[n], {n, -1, z}]]

%t Flatten[Table[g[n], {n, -1, z}]]  (* A193903 *)

%Y Cf. A193722, A193902.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 08 2011