A193894 - OEIS

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

%S 1,4,2,44,28,12,210,150,90,36,680,520,360,208,80,1750,1400,1050,710,

%T 400,150,3864,3192,2520,1860,1236,684,252,7644,6468,5292,4130,3010,

%U 1974,1078,392,13920,12000,10080,8176,6320,4560,2960,1600,576,23760

%N Mirror of the triangle A193893.

%C A193894 is obtained by reversing the rows of the triangle A193893.

%F Write w(n,k) for the triangle at A193893.  The triangle at A193894 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 4.....2

%e 44....28....12

%e 210...150...90....36

%e 680...520...360...208..80

%e 1750..1400..1050..710..400..105

%t z = 9;

%t p[n_, x_] := Sum[(k + 1) (n + 1)*x^(n - 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}]]  (* A193893 *)

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

%t Flatten[Table[g[n], {n, -1, z}]]  (* A193894 *)

%Y Cf. A193893.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 08 2011