cp's OEIS Frontend

A193851 Mirror of the triangle A193850.

%I A193851 #5 Mar 30 2012 18:57:38
%S A193851 2,8,4,26,20,8,80,72,48,16,242,232,192,112,32,728,716,656,496,256,64,
%T A193851 2186,2172,2088,1808,1248,576,128,6560,6544,6432,5984,4864,3072,1280,
%U A193851 256,19682,19664,19520,18848,16832,12800,7424,2816,512,59048,59028
%N A193851 Mirror of the triangle A193850.
%C A193851 A193851 is obtained by reversing the rows of the triangle A193850.
%F A193851 Write w(n,k) for the triangle at A193850.  The triangle at A193851 is then given by w(n,n-k).
%e A193851 First six rows:
%e A193851 2
%e A193851 8....4
%e A193851 26...20....8
%e A193851 80...72...40..16
%e A193851 242...232...192...112...32
%e A193851 728...716...656...496..256..64
%t A193851 z = 10;
%t A193851 p[n_, x_] := (x + 2)^n;
%t A193851 q[0, x_] := 1; q[n_, x_] := x*q[n - 1, x] + 1;
%t A193851 p1[n_, k_] := Coefficient[p[n, x], x^k];
%t A193851 p1[n_, 0] := p[n, x] /. x -> 0;
%t A193851 d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
%t A193851 h[n_] := CoefficientList[d[n, x], {x}]
%t A193851 TableForm[Table[Reverse[h[n]], {n, 0, z}]]
%t A193851 Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193850 *)
%t A193851 TableForm[Table[h[n], {n, 0, z}]]
%t A193851 Flatten[Table[h[n], {n, -1, z}]]   (* A193851  *)
%t A193851 TableForm[Table[Reverse[h[n]/2], {n, 0, z}]]
%t A193851 Flatten[Table[Reverse[h[n]]/2, {n, -1, z}]] (* A193852 *)
%t A193851 TableForm[Table[h[n]/2, {n, 0, z}]]
%t A193851 Flatten[Table[h[n]/2, {n, -1, z}]]  (* A193853 *)
%Y A193851 Cf. A193850, A193853.
%K A193851 nonn,tabl
%O A193851 0,1
%A A193851 _Clark Kimberling_, Aug 07 2011