A193966 - OEIS

%I #6 Mar 30 2012 18:57:39

%S 1,3,1,15,10,3,43,26,15,4,120,75,43,25,7,318,196,120,69,40,11,840,520,

%T 318,195,112,65,18,2203,1361,840,514,315,181,105,29,5775,3570,2203,

%U 1360,832,510,293,170,47,15123,9346,5775,3564,2200,1346,825,474

%N Mirror of the triangle A193965.

%C A193966 is obtained by reversing the rows of the triangle A193965.

%F Write w(n,k) for the triangle at A193965.  The triangle at A193966 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 3.....1

%e 15....10...3

%e 43....26...15...4

%e 120...75...43...25..7

%e 318...196..120..69..40..11

%t z = 12;

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

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

%t t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := 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}]]  (* A193965 *)

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

%t Flatten[Table[g[n], {n, -1, z}]]  (* A193966 *)

%Y Cf. A193965.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 10 2011