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A193892 Mirror of the triangle A193891. 2

%I

%S 1,2,1,8,5,2,20,14,8,3,40,30,20,11,4,70,55,40,26,14,5,112,91,70,50,32,

%T 17,6,168,140,112,85,60,38,20,7,240,204,168,133,100,70,44,23,8,330,

%U 285,240,196,154,115,80,50,26,9,440,385,330,276,224,175,130,90,56

%N Mirror of the triangle A193891.

%C A193892 is obtained by reversing the rows of the triangle A193891.

%F Write w(n,k) for the triangle at A193891. The triangle at A193892 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 2....1

%e 8....5....2

%e 20...14...8....3

%e 40...30...20...11...4

%e 70...55...40...26...14...5

%t z = 9;

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

%t q[n_, x_] := p[n, x];

%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}]] (* A193891 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193892 *)

%Y Cf. A193891.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 08 2011

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Last modified September 18 23:45 EDT 2021. Contains 347549 sequences. (Running on oeis4.)