A193859 - OEIS

%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