cp's OEIS Frontend

A193861 Mirror of the triangle A193860.

%I A193861 #5 Mar 30 2012 18:57:39
%S A193861 1,5,1,19,7,1,65,33,9,1,211,131,51,11,1,665,473,233,73,13,1,2059,1611,
%T A193861 939,379,99,15,1,6305,5281,3489,1697,577,129,17,1,19171,16867,12259,
%U A193861 6883,2851,835,163,19,1,58025,52905,41385,26025,12585,4521,1161
%N A193861 Mirror of the triangle A193860.
%C A193861 A193861 is obtained by reversing the rows of the triangle A193860.
%F A193861 Write w(n,k) for the triangle at A193860.  The triangle at A193861 is then given by w(n,n-k).
%e A193861 First six rows:
%e A193861 1
%e A193861 5.....1
%e A193861 19....7.....1
%e A193861 65....33....9.....1
%e A193861 211...131...51....11...1
%e A193861 665...473...233...73...13...1
%t A193861 z = 10;
%t A193861 p[n_, x_] := (2 x + 1)^n;
%t A193861 q[0, x_] := 1; q[n_, x_] := x*q[n - 1, x] + 1;
%t A193861 p1[n_, k_] := Coefficient[p[n, x], x^k];
%t A193861 p1[n_, 0] := p[n, x] /. x -> 0;
%t A193861 d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
%t A193861 h[n_] := CoefficientList[d[n, x], {x}]
%t A193861 TableForm[Table[Reverse[h[n]], {n, 0, z}]]
%t A193861 Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193860 *)
%t A193861 TableForm[Table[h[n], {n, 0, z}]]
%t A193861 Flatten[Table[h[n], {n, -1, z}]]   (* A193861  *)
%Y A193861 Cf. A193860.
%K A193861 nonn,tabl
%O A193861 0,2
%A A193861 _Clark Kimberling_, Aug 07 2011