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A193595 Augmentation of the Fibonacci triangle A058071. See Comments.

%I A193595 #5 Mar 30 2012 18:57:38
%S A193595 1,1,1,2,2,3,6,8,9,13,30,42,58,56,85,240,360,480,576,533,821,3120,
%T A193595 4800,6600,7488,8698,7666,12015,65520,102960,141120,165240,178158,
%U A193595 200200,171501,271601,2227680,3538080,4876560,5670720,6310590,6513474
%N A193595 Augmentation of the Fibonacci triangle A058071.  See Comments.
%C A193595 For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
%C A193595 Regarding A193595, (column 1)=A003266, (column 2)=A191994.
%e A193595 First 5 rows of A193589:
%e A193595 1
%e A193595 1....1
%e A193595 2....2....3
%e A193595 6....8....9....13
%e A193595 30...42...58...56...85
%t A193595 p[n_, k_] := Fibonacci[k + 1]*Fibonacci[n + 1 - k]
%t A193595 Table[p[n, k], {n, 0, 5}, {k, 0,
%t A193595   n}]  (* A058071, a Fibonacci triangle *)
%t A193595 m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
%t A193595 TableForm[m[4]]
%t A193595 w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
%t A193595 v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
%t A193595 v[n_] := v[n - 1].m[n]
%t A193595 TableForm[Table[v[n], {n, 0, 10}]]  (* A193595 *)
%t A193595 Flatten[Table[v[n], {n, 0, 9}]]
%Y A193595 Cf. A193091, A058071, A003266, A191994.
%K A193595 nonn,tabl
%O A193595 0,4
%A A193595 _Clark Kimberling_, Jul 31 2011