A193741 - OEIS

%I #5 Mar 30 2012 18:57:38

%S 1,1,1,3,3,1,9,9,4,1,19,19,10,4,1,34,34,20,10,4,1,55,55,35,20,10,4,1,

%T 83,83,56,35,20,10,4,1,119,119,84,56,35,20,10,4,1,164,164,120,84,56,

%U 35,20,10,4,1,219,219,165,120,84,56,35,20,10,4,1,285,285,220,165

%N Mirror of the triangle A193740.

%C A193741 is obtained by reversing the rows of the triangle A193740.

%F Write w(n,k) for the triangle at A193740.  The triangle at A193741 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1....1

%e 3....3....1

%e 9....9....4....1

%e 19...19...10...4...1

%e 34...34...20...10..4..1

%t z = 12;

%t p[0, x_] := 1

%t p[n_, x_] := n + Sum[(k + 1) x^(n - k), {k, 0, n - 1}]

%t q[n_, x_] := p[n, x]

%t t[n_, k_] := Coefficient[p[n, x], x^(n - k)];

%t t[n_, n_] := p[n, x] /. x -> 0;

%t w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1

%t g[n_] := CoefficientList[w[n, x], {x}]

%t TableForm[Table[Reverse[g[n]], {n, -1, z}]]

%t Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193740 *)

%t TableForm[Table[g[n], {n, -1, z}]]

%t Flatten[Table[g[n], {n, -1, z}]]   (* A193741 *)

%Y Cf. A193740.

%K nonn,tabl

%O 0,4

%A _Clark Kimberling_, Aug 04 2011