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%I #6 Mar 30 2012 18:57:39
%S 1,1,3,3,10,15,4,15,26,43,7,25,43,75,120,11,40,69,120,196,318,18,65,
%T 112,195,318,520,840,29,105,181,315,514,840,1361,2203,47,170,293,510,
%U 832,1360,2203,3570,5775,76,275,474,825,1346,2200,3564,5775,9346
%N Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{L(k+1)*x^(n-k) : 0<=k<=n}, where L=A000032 (Lucas numbers).
%C See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
%e First six rows:
%e 1
%e 1...3
%e 3...10...15
%e 4...15...26...43
%e 7...25...43...75...120
%e 11..40...69...120..196..318
%t z = 12;
%t p[n_, x_] := Sum[LucasL[k + 1]*x^(n - k), {k, 0, n}];
%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}]] (* A193965 *)
%t TableForm[Table[g[n], {n, -1, z}]]
%t Flatten[Table[g[n], {n, -1, z}]] (* A193966 *)
%Y Cf. A193722, A193966.
%K nonn,tabl
%O 0,3
%A _Clark Kimberling_, Aug 10 2011