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%I #6 Mar 30 2012 18:57:39
%S 1,3,2,7,10,4,15,34,28,8,31,98,124,72,16,63,258,444,392,176,32,127,
%T 642,1404,1672,1136,416,64,255,1538,4092,6152,5616,3104,960,128,511,
%U 3586,11260,20488,23536,17440,8128,2176,256,1023,8194,29692,63496
%N Mirror of the triangle A193858.
%C A193859 is obtained by reversing the rows of the triangle A193858.
%F Write w(n,k) for the triangle at A193858. The triangle at A193859 is then given by w(n,n-k).
%e First six rows:
%e 1
%e 3....2
%e 7....10...4
%e 15...34...28...8
%e 31...98...124..72...16
%e 63...258..444..392..176..32
%t z = 10;
%t p[n_, x_] := (x + 1)^n;
%t q[n_, x_] := (2 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}]] (* A193858 *)
%t TableForm[Table[h[n], {n, 0, z}]]
%t Flatten[Table[h[n], {n, -1, z}]] (* A193859 *)
%Y Cf. A193858.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_, Aug 07 2011
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