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Mirror of the triangle A193953.
2

%I #5 Mar 30 2012 18:57:39

%S 1,2,1,5,3,1,13,9,5,2,28,21,14,8,3,58,46,34,23,13,5,114,94,74,55,37,

%T 21,8,218,185,152,120,89,60,34,13,407,353,299,246,194,144,97,55,21,

%U 747,659,571,484,398,314,233,157,89,34,1352,1209,1066,924,783,644

%N Mirror of the triangle A193953.

%C A193954 is obtained by reversing the rows of the triangle A193953.

%F Write w(n,k) for the triangle at A193953. The triangle at A193954 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 2....1

%e 5....3....1

%e 13...9....5....2

%e 28...21...14...8...3

%e 58...46...34...23..13..5

%t z = 12;

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

%t q[n_, x_] := x*q[n - 1, x] + n + 1; q[0, x_] := 1

%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}]] (* A193953 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193954 *)

%Y Cf. A193953.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 10 2011