cp's OEIS Frontend

A193822 Mirror of the triangle A193821.

%I A193822 #6 Mar 30 2012 18:57:38
%S A193822 1,1,1,3,3,2,9,9,8,4,27,27,26,20,8,81,81,80,72,48,16,243,243,242,232,
%T A193822 192,112,32,729,729,728,716,656,496,256,64,2187,2187,2186,2172,2088,
%U A193822 1808,1248,576,128,6561,6561,6560,6544,6432,5984,4864,3072,1280,256
%N A193822 Mirror of the triangle A193821.
%C A193822 A193822 is obtained by reversing the rows of the triangle A193821.
%F A193822 Write w(n,k) for the triangle at A193821.  The triangle at A193822 is then given by w(n,n-k).
%e A193822 First six rows:
%e A193822 1
%e A193822 1....1
%e A193822 3....3....2
%e A193822 9....9....8.....4
%e A193822 27...27...26....20...8
%e A193822 81...81...80....72...48...16
%t A193822 p[n_, x_] := (a*x + b)^n
%t A193822 q[0, x_] := 1
%t A193822 q[n_, x_] := x*q[n - 1, x] + 1; q[n_, 0] := q[n, x] /. x -> 0;
%t A193822 t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
%t A193822 w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
%t A193822 g[n_] := CoefficientList[w[n, x], {x}]
%t A193822 TableForm[Table[Reverse[g[n]], {n, -1, z}]]
%t A193822 Flatten[Table[Reverse[g[n]], {n, -1, z}]]   (* A193821 *)
%t A193822 TableForm[Table[g[n], {n, -1, z}]]
%t A193822 Flatten[Table[g[n], {n, -1, z}]]  (* A193822 *)
%Y A193822 Cf. A193722, A193821.
%K A193822 nonn,tabl
%O A193822 0,4
%A A193822 _Clark Kimberling_, Aug 06 2011