%I #5 Mar 30 2012 18:57:39
%S 1,4,1,13,5,1,45,23,9,2,120,71,36,14,3,300,196,116,59,23,5,692,484,
%T 316,187,95,37,8,1524,1121,784,512,303,154,60,13,3225,2465,1813,1268,
%U 828,490,249,97,21,6625,5219,3989,2934,2052,1340,793,403,157,34,13280
%N Mirror of the triangle A193955.
%C A193956 is obtained by reversing the rows of the triangle A193955.
%F Write w(n,k) for the triangle at A193955. The triangle at A193955 is then given by w(n,n-k).
%e First six rows:
%e 1
%e 4.....1
%e 13....5....1
%e 45....23...9....2
%e 120...71...36...14..3
%e 300...192..116..59..23..5
%t z = 12;
%t p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
%t q[n_, x_] := Sum[((k + 1)^2)*x^(n - k), {k, 0, n}] ;
%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}]] (* A193955 *)
%t TableForm[Table[g[n], {n, -1, z}]]
%t Flatten[Table[g[n], {n, -1, z}]] (* A193956 *)
%Y Cf. A193955.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_, Aug 10 2011