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A193960 Mirror of the triangle A193959. 2

%I

%S 1,1,1,9,5,4,36,23,13,9,116,71,45,25,16,316,196,120,75,41,25,784,484,

%T 300,183,113,61,36,1813,1121,692,428,260,159,85,49,3989,2465,1524,940,

%U 580,351,213,113,64,8444,5219,3225,1993,1228,756,456,275,145,81

%N Mirror of the triangle A193959.

%C A193960 is obtained by reversing the rows of the triangle A193959.

%F Write w(n,k) for the triangle at A193959. The triangle at A193960 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1.....1

%e 9.....5....4

%e 36....23...13...9

%e 116...71...45...25..16

%e 316...196..120..75..41..25

%t z = 12;

%t p[n_, x_] := Sum[((k + 1)^2)*x^(n - k), {k, 0, n}]

%t q[n_, x_] := Sum[Fibonacci[k + 1]*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}]] (* A193959 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193960 *)

%Y Cf. A193959.

%K nonn,tabl

%O 0,4

%A _Clark Kimberling_, Aug 10 2011

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Last modified May 16 05:56 EDT 2022. Contains 353693 sequences. (Running on oeis4.)