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Mirror of the triangle A193963.
2

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

%S 1,1,4,5,20,9,14,56,45,16,30,120,126,80,25,55,220,270,224,125,36,91,

%T 364,495,480,350,180,49,140,560,819,880,750,504,245,64,204,816,1260,

%U 1456,1375,1080,686,320,81,285,1140,1836,2240,2275,1980,1470,896

%N Mirror of the triangle A193963.

%C A193964 is obtained by reversing the rows of the triangle A193963.

%F Write w(n,k) for the triangle at A193963. The triangle at A193964 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1....4

%e 5....20....9

%e 14...56....45....16

%e 30...120...126...80....25

%e 55...220...270...224...125...36

%t p[n_, x_] := Sum[((k + 1)^2)*x^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}]] (* A193963 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193964 *)

%Y Cf. A193963.

%K nonn,tabl

%O 0,3

%A _Clark Kimberling_, Aug 10 2011