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A193962 Mirror of the triangle A193961. 2

%I #5 Mar 30 2012 18:57:39

%S 1,4,1,40,17,4,184,98,40,9,584,354,184,73,16,1484,979,584,298,116,25,

%T 3248,2275,1484,874,440,169,36,6384,4676,3248,2099,1224,610,232,49,

%U 11568,8772,6384,4403,2824,1634,808,305,64,19668,15333,11568,8372

%N Mirror of the triangle A193961.

%C A193962 is obtained by reversing the rows of the triangle A193961.

%F Write w(n,k) for the triangle at A193961. The triangle at A193962 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 4......1

%e 40.....17....4

%e 184....98....40....9

%e 584....354...184...73...16

%e 1484...979...584...298..116..25

%t z = 12;

%t p[n_, x_] := Sum[((k + 1)^2)*x^(n - k), {k, 0, n}]

%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}]] (* A193961 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193962 *)

%Y Cf. A193961.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 10 2011

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Last modified July 15 23:38 EDT 2024. Contains 374343 sequences. (Running on oeis4.)