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%I #5 Mar 30 2012 18:57:39
%S 1,1,2,2,5,10,4,10,21,42,8,20,42,85,170,16,40,84,170,341,682,32,80,
%T 168,340,682,1365,2730,64,160,336,680,1364,2730,5461,10922,128,320,
%U 672,1360,2728,5460,10922,21845,43690,256,640,1344,2720,5456,10920
%N Triangular array: the self-fusion of (p(n,x)), where p(n,x)=x*p(n-1,x)+2^n, 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 A193897:
%e 1
%e 1....2
%e 2....5....10
%e 4....10...21...42
%e 8....20...42...85....170
%e 16...40...84...170...341...682
%t z = 12;
%t p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 1;
%t q[n_, x_] := p[n, x];
%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}]] (* A193899 *)
%t TableForm[Table[g[n], {n, -1, z}]]
%t Flatten[Table[g[n], {n, -1, z}]] (* A193900 *)
%Y Cf. A193722, A193900.
%K nonn,tabl
%O 0,3
%A _Clark Kimberling_, Aug 08 2011
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