cp's OEIS Frontend

A193824 Mirror of the triangle A193823.

%I A193824 #5 Mar 30 2012 18:57:38
%S A193824 1,1,1,3,3,1,9,9,5,1,27,27,19,7,1,81,81,65,33,9,1,243,243,211,131,51,
%T A193824 11,1,729,729,665,473,233,73,13,1,2187,2187,2059,1611,939,379,99,15,1,
%U A193824 6561,6561,6305,5281,3489,1697,577,129,17,1,19683,19683,19171
%N A193824 Mirror of the triangle A193823.
%C A193824 A193824 is obtained by reversing the rows of the triangle A193823.
%F A193824 Write w(n,k) for the triangle at A193823.  The triangle at A193824 is then given by w(n,n-k).
%e A193824 First six rows:
%e A193824 1
%e A193824 1....1
%e A193824 3....3....1
%e A193824 9....9....5.....1
%e A193824 27...27...19....7...1
%e A193824 81...81...65....33...9...1
%t A193824 z = 10; a = 2; b = 1;
%t A193824 p[n_, x_] := (a*x + b)^n
%t A193824 q[0, x_] := 1
%t A193824 q[n_, x_] := x*q[n - 1, x] + 1; q[n_, 0] := q[n, x] /. x -> 0;
%t A193824 t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
%t A193824 w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
%t A193824 g[n_] := CoefficientList[w[n, x], {x}]
%t A193824 TableForm[Table[Reverse[g[n]], {n, -1, z}]]
%t A193824 Flatten[Table[Reverse[g[n]], {n, -1, z}]]   (* A193823 *)
%t A193824 TableForm[Table[g[n], {n, -1, z}]]
%t A193824 Flatten[Table[g[n], {n, -1, z}]]  (* A193824 *)
%Y A193824 Cf. A193823.
%K A193824 nonn,tabl
%O A193824 0,4
%A A193824 _Clark Kimberling_, Aug 06 2011