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%I #5 Mar 30 2012 18:57:39
%S 1,4,1,9,20,5,16,45,56,14,25,80,126,120,30,36,125,224,270,220,55,49,
%T 180,350,480,495,364,91,64,245,504,750,880,819,560,140,81,320,686,
%U 1080,1375,1456,1260,816,204,100,405,896,1470,1980,2275,2240,1836,1140
%N Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{((k+1)^2)*x^k : 0<=k<=n}.
%C See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
%e First six rows:
%e 1
%e 4....1
%e 9....20....5
%e 16...45....56....14
%e 25...80....126...120...30
%e 36...125...224...270...220...55
%t z = 12;
%t p[n_, x_] := Sum[((k + 1)^2)*x^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}]] (* A193963 *)
%t TableForm[Table[g[n], {n, -1, z}]]
%t Flatten[Table[g[n], {n, -1, z}]] (* A193964 *)
%Y Cf. A193722, A193964.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_, Aug 10 2011
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