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%I #5 Mar 30 2012 18:57:39
%S 2,5,3,9,11,4,14,26,19,5,20,50,55,29,6,27,85,125,99,41,7,35,133,245,
%T 259,161,55,8,44,196,434,574,476,244,71,9,54,276,714,1134,1176,804,
%U 351,89,10,65,375,1110,2058,2562,2190,1275,485,109,11,77,495,1650
%N Mirror of the triangle A193971.
%C A193972 is obtained by reversing the rows of the triangle A193971.
%F Write w(n,k) for the triangle at A193971. The triangle at A193972 is then given by w(n,n-k).
%e First six rows:
%e 2
%e 5....3
%e 9....11...4
%e 14...26...19....5
%e 20...50...55....29...6
%e 27...85...125...99...41...7
%t z = 11;
%t p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
%t q[n_, x_] := (x + 1)^n
%t p1[n_, k_] := Coefficient[p[n, x], x^k];
%t p1[n_, 0] := p[n, x] /. x -> 0;
%t d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
%t h[n_] := CoefficientList[d[n, x], {x}]
%t TableForm[Table[Reverse[h[n]], {n, 0, z}]]
%t Flatten[Table[Reverse[h[n]], {n, -1, z}]] (* A193971 *)
%t TableForm[Table[h[n], {n, 0, z}]]
%t Flatten[Table[h[n], {n, -1, z}]] (* A193972 *)
%Y Cf. A193971.
%K nonn,tabl
%O 0,1
%A _Clark Kimberling_, Aug 10 2011
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