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%I #5 Mar 30 2012 18:57:39
%S 1,1,2,3,6,3,6,12,9,4,10,20,18,12,5,15,30,30,24,15,6,21,42,45,40,30,
%T 18,7,28,56,63,60,50,36,21,8,36,72,84,84,75,60,42,24,9,45,90,108,112,
%U 105,90,70,48,27,10,55,110,135,144,140,126,105,80,54,30,11,66,132
%N Mirror of the triangle A193897.
%C A193898 is obtained by reversing the rows of the triangle A193897.
%F Write w(n,k) for the triangle at A193897. The triangle at A193898 is then given by w(n,n-k).
%e First six rows:
%e 1
%e 1....2
%e 3....6....3
%e 6....12...9....4
%e 10...20...18...12...5
%e 15...30...30...24...15...6
%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. A193897.
%K nonn,tabl
%O 0,3
%A _Clark Kimberling_, Aug 08 2011
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