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A193978 Mirror of the triangle A193977.

%I A193978 #5 Mar 30 2012 18:57:39
%S A193978 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 A193978 104,105,90,56,44,84,117,140,150,144,119,72,54,104,147,180,200,204,
%U A193978 189,152,90,65,126,180,224,255,270,266,240,189,110,77,150,216,272
%N A193978 Mirror of the triangle A193977.
%C A193978 A193978 is obtained by reversing the rows of the triangle A193977.
%F A193978 Write w(n,k) for the triangle at A193977.  The triangle at A193978 is then given by w(n,n-k).
%e A193978 First six rows:
%e A193978 2
%e A193978 5....6
%e A193978 9....14...12
%e A193978 14...24...27...20
%e A193978 20...36...45...44...30
%e A193978 27...50...66...72...65...42
%t A193978 z = 11;
%t A193978 p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
%t A193978 q[n_, x_] := Sum[(k + 1)*x^k, {k, 0, n}]
%t A193978 p1[n_, k_] := Coefficient[p[n, x], x^k];
%t A193978 p1[n_, 0] := p[n, x] /. x -> 0;
%t A193978 d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
%t A193978 h[n_] := CoefficientList[d[n, x], {x}]
%t A193978 TableForm[Table[Reverse[h[n]], {n, 0, z}]]
%t A193978 Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193977 *)
%t A193978 TableForm[Table[h[n], {n, 0, z}]]
%t A193978 Flatten[Table[h[n], {n, -1, z}]]  (* A193978 *)
%Y A193978 Cf. A193977.
%K A193978 nonn,tabl
%O A193978 0,1
%A A193978 _Clark Kimberling_, Aug 10 2011