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%I #5 Mar 30 2012 18:57:39
%S 1,2,1,3,6,3,4,9,12,6,5,12,18,20,10,6,15,24,30,30,15,7,18,30,40,45,42,
%T 21,8,21,36,50,60,63,56,28,9,24,42,60,75,84,84,72,36,10,27,48,70,90,
%U 105,112,108,90,45,11,30,54,80,105,126,140,144,135,110,55,12,33
%N Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{(k+1)*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 of A193897:
%e 1
%e 2...1
%e 3...6....3
%e 4...9....12...6
%e 5...12...18...20...10
%e 6...15...24...30...30...15
%t z = 12;
%t p[n_, x_] := (n + 1)*x^n + p[n - 1, x] (* #7 *); p[0, x_] := 1;
%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}]] (* A193897 *)
%t TableForm[Table[g[n], {n, -1, z}]]
%t Flatten[Table[g[n], {n, -1, z}]] (* A193898 *)
%Y Cf. A193722, A193898.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_, Aug 08 2011
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