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%I #5 Mar 30 2012 18:57:39
%S 1,2,1,10,5,2,42,21,10,4,170,85,42,20,8,682,341,170,84,40,16,2730,
%T 1365,682,340,168,80,32,10922,5461,2730,1364,680,336,160,64,43690,
%U 21845,10922,5460,2728,1360,672,320,128,174762,87381,43690,21844,10920
%N Mirror of the triangle A193899.
%C A193900 is obtained by reversing the rows of the triangle A193899.
%F Write w(n,k) for the triangle at A193899. The triangle at A193900 is then given by w(n,n-k).
%e First six rows:
%e 1
%e 2.....1
%e 10....5....2
%e 42....21...10...4
%e 170...85...42...20..8
%e 682...341..170..84..40..16
%t z = 12;
%t p[n_, x_] := x*p[n - 1, x] + 2^n; 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}]] (* A193899 *)
%t TableForm[Table[g[n], {n, -1, z}]]
%t Flatten[Table[g[n], {n, -1, z}]] (* A193900 *)
%Y Cf. A193899.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_, Aug 08 2011
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