A193792 - OEIS

%I #4 Mar 30 2012 18:57:38

%S 1,1,1,3,1,4,9,6,1,16,27,27,9,1,64,81,108,54,12,1,256,243,405,270,90,

%T 15,1,1024,729,1458,1215,540,135,18,1,4096,2187,5103,5103,2835,945,

%U 189,21,1,16384,6561,17496,20412,13608,5670,1512,252,24,1,65536

%N Triangular array:  the fusion of polynomial sequences P and Q given by p(n,x)=(x+3)^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 3....1....4

%e 9....6....1....16

%e 27...27...9....1...64

%e 81...108..54...12..1...256

%t z = 8; a = 1; b = 3;

%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}]]  (* A193792 *)

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

%t Flatten[Table[g[n], {n, -1, z}]]  (* A193793 *)

%Y Cf. A193722, A193733.

%K nonn,tabl

%O 0,4

%A _Clark Kimberling_, Aug 05 2011