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 A193896 Mirror of the triangle A193895. 2

%I

%S 1,1,2,3,6,6,6,12,15,12,10,20,27,28,20,15,30,42,48,45,30,21,42,60,72,

%T 75,66,42,28,56,81,100,110,108,91,56,36,72,105,132,150,156,147,120,72,

%U 45,90,132,168,195,210,210,192,153,90,55,110,162,208,245,270,280

%N Mirror of the triangle A193895.

%C A193896 is obtained by reversing the rows of the triangle A193895.

%F Write w(n,k) for the triangle at A193895. The triangle at A193896 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1....2

%e 3....6....6

%e 6....12...15...12

%e 10...20...27...28...20

%e 15...30...42...48...45...30

%t z = 9;

%t p[n_, x_] := x*p[n - 1, x] + n + 1 (* #6 *) ; p[0, x_] := 1;

%t q[n_, x_] := (n + 1)*x^n + q[n - 1, x] (* #7 *); q[0, x_] := 1;

%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}]] (* A193895 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193896 *)

%Y Cf. A193895.

%K nonn,tabl

%O 0,3

%A _Clark Kimberling_, Aug 08 2011

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Last modified December 9 07:21 EST 2021. Contains 349627 sequences. (Running on oeis4.)