cp's OEIS Frontend

A193788 Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(x+1)^n and q(n,x)=1+x^n.

%I A193788 #4 Mar 30 2012 18:57:38
%S A193788 1,1,1,2,1,3,4,4,1,9,8,12,6,1,27,16,32,24,8,1,81,32,80,80,40,10,1,243,
%T A193788 64,192,240,160,60,12,1,729,128,448,672,560,280,84,14,1,2187,256,1024,
%U A193788 1792,1792,1120,448,112,16,1,6561,512,2304,4608,5376,4032,2016
%N A193788 Triangular array:  the fusion of polynomial sequences P and Q given by p(n,x)=(x+1)^n and q(n,x)=1+x^n.
%C A193788 See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
%e A193788 First six rows:
%e A193788 1
%e A193788 1....1
%e A193788 2....1....3
%e A193788 4....4....1....9
%e A193788 8....12...6....1...27
%e A193788 16...32...24...8...1...81
%e A193788  (viz., A038207 with row sums at end of rows)
%t A193788 z = 10; a = 1; b = 2;
%t A193788 p[n_, x_] := (a*x + b)^n
%t A193788 q[n_, x_] := 1 + x^n ; q[n_, 0] := q[n, x] /. x -> 0;
%t A193788 t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
%t A193788 w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
%t A193788 g[n_] := CoefficientList[w[n, x], {x}]
%t A193788 TableForm[Table[Reverse[g[n]], {n, -1, z}]]
%t A193788 Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193788 *)
%t A193788 TableForm[Table[g[n], {n, -1, z}]]
%t A193788 Flatten[Table[g[n], {n, -1, z}]]  (* A193789 *)
%Y A193788 Cf. A193722, A038207, A193789.
%K A193788 nonn,tabl
%O A193788 0,4
%A A193788 _Clark Kimberling_, Aug 05 2011