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 A193920 Mirror of the triangle A193919. 2

%I

%S 1,1,1,2,3,1,4,9,7,2,7,21,25,14,3,12,46,75,64,28,5,20,94,195,224,148,

%T 53,8,33,185,468,679,603,326,99,13,54,353,1056,1855,2073,1502,687,181,

%U 21,88,659,2280,4711,6357,5786,3543,1405,327,34,143,1209,4755

%N Mirror of the triangle A193919.

%C A193920 is obtained by reversing the rows of the triangle A193919.

%F Write w(n,k) for the triangle at A193919. The triangle at A193920 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1....1

%e 2....3....1

%e 4....9....7....2

%e 7....21...25...14...3

%e 12...46...75...64...28...5

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

%t q[n_, x_] := (x + 1)^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}]] (* A193919 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193920 *)

%Y Cf. A193919.

%K nonn,tabl

%O 0,4

%A _Clark Kimberling_, Aug 09 2011

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Last modified May 28 15:55 EDT 2020. Contains 334684 sequences. (Running on oeis4.)