A173504 - OEIS

%I #8 Apr 26 2021 01:54:43

%S 1,1,1,1,2,1,1,16,16,1,1,416,3328,416,1,1,33280,6922240,6922240,33280,

%T 1,1,8053760,134014566400,3484378726400,134014566400,8053760,1,1,

%U 5863137280,23610150250086400,49109112520179712000,49109112520179712000,23610150250086400,5863137280,1

%N Triangle T(n, k, q) = c(n, q)/(c(k, q)*c(n-k, q)) where c(n,q) = Product_{j=1..n} (q^j -1)^(n-j) and q = 3, read by rows.

%H G. C. Greubel, <a href="/A173504/b173504.txt">Rows n = 0..23 of the triangle, flattened</a>

%F T(n, k, q) = c(n, q)/(c(k, q)*c(n-k, q)) where c(n,q) = Product_{j=1..n} (q^j -1)^(n-j) and q = 3.

%e The triangle begins as:

%e   1;

%e   1,       1;

%e   1,       2,            1;

%e   1,      16,           16,             1;

%e   1,     416,         3328,           416,            1;

%e   1,   33280,      6922240,       6922240,        33280,       1;

%e   1, 8053760, 134014566400, 3484378726400, 134014566400, 8053760, 1;

%t c[n_, q_]:= Product[(q^m-1)^(n-m), {m,1,n}];

%t T[n_, k_, q_]:= c[n, q]/(c[k, q]*c[n-k, q]);

%t Table[T[n, k, 3], {n,0,10}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Apr 25 2021 *)

%o (Sage)

%o @CachedFunction

%o def c(n,q): return product( (q^j -1)^(n-j) for j in (1..n))

%o def T(n,k,q): return c(n,q)/(c(k,q)*c(n-k,q))

%o flatten([[T(n,k,3) for k in (0..n)] for n in (0..10)]) # _G. C. Greubel_, Apr 25 2021

%Y Cf. A173503, A173505.

%K nonn,tabl,less

%O 0,5

%A _Roger L. Bagula_, Feb 20 2010

%E Edited by _G. C. Greubel_, Apr 25 2021