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%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