A193978 - OEIS

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

%S 2,5,6,9,14,12,14,24,27,20,20,36,45,44,30,27,50,66,72,65,42,35,66,90,

%T 104,105,90,56,44,84,117,140,150,144,119,72,54,104,147,180,200,204,

%U 189,152,90,65,126,180,224,255,270,266,240,189,110,77,150,216,272

%N Mirror of the triangle A193977.

%C A193978 is obtained by reversing the rows of the triangle A193977.

%F Write w(n,k) for the triangle at A193977.  The triangle at A193978 is then given by w(n,n-k).

%e First six rows:

%e 2

%e 5....6

%e 9....14...12

%e 14...24...27...20

%e 20...36...45...44...30

%e 27...50...66...72...65...42

%t z = 11;

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

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

%t p1[n_, k_] := Coefficient[p[n, x], x^k];

%t p1[n_, 0] := p[n, x] /. x -> 0;

%t d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]

%t h[n_] := CoefficientList[d[n, x], {x}]

%t TableForm[Table[Reverse[h[n]], {n, 0, z}]]

%t Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193977 *)

%t TableForm[Table[h[n], {n, 0, z}]]

%t Flatten[Table[h[n], {n, -1, z}]]  (* A193978 *)

%Y Cf. A193977.

%K nonn,tabl

%O 0,1

%A _Clark Kimberling_, Aug 10 2011