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%I #5 Mar 30 2012 18:57:39
%S 1,5,1,19,8,1,65,43,11,1,211,194,76,14,1,665,793,422,118,17,1,2059,
%T 3044,2059,776,169,20,1,6305,11191,9221,4387,1283,229,23,1,19171,
%U 39878,38854,22382,8236,1970,298,26,1,58025,138805,156440,106000,47090
%N Mirror of the triangle A193856.
%C A193857 is obtained by reversing the rows of the triangle A193856.
%F Write w(n,k) for the triangle at A193856. The triangle at A193857 is then given by w(n,n-k).
%e First six rows:
%e 1
%e 5.....1
%e 19....8.....1
%e 65....43....11....1
%e 211...194...76....14....1
%e 665...793...422...118...17...1
%t z = 10;
%t p[n_, x_] := (2 x + 1)^n;
%t q[n_, x_] := (x + 1)^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}]] (* A193856 *)
%t TableForm[Table[h[n], {n, 0, z}]]
%t Flatten[Table[h[n], {n, -1, z}]] (* A193857 *)
%Y Cf. A193856.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_, Aug 07 2011
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