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%I
%S 1,1,1,2,3,5,4,12,9,25,8,36,54,27,125,16,96,216,216,81,625,32,240,720,
%T 1080,810,243,3125,64,576,2160,4320,4860,2916,729,15625,128,1344,6048,
%U 15120,22680,20412,10206,2187,78125,256,3072,16128,48384,90720
%N Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(3x+2)^n and q(n,x)=1+x^n.
%C See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
%e First six rows:
%e 1
%e 1....1
%e 2....3....5
%e 4....12...9.....25
%e 8....36...54....27...125
%e 16...96...216...216..81...625
%t z = 8; a = 3; b = 2;
%t p[n_, x_] := (a*x + b)^n
%t q[n_, x_] := 1 + x^n ; q[n_, 0] := q[n, x] /. x -> 0;
%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}]] (* A193798 *)
%t TableForm[Table[g[n], {n, -1, z}]]
%t Flatten[Table[g[n], {n, -1, z}]] (* A193799 *)
%Y Cf. A193722, A193799.
%K nonn,tabl
%O 0,4
%A _Clark Kimberling_, Aug 05 2011
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