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A173504 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. 2
1, 1, 1, 1, 2, 1, 1, 16, 16, 1, 1, 416, 3328, 416, 1, 1, 33280, 6922240, 6922240, 33280, 1, 1, 8053760, 134014566400, 3484378726400, 134014566400, 8053760, 1, 1, 5863137280, 23610150250086400, 49109112520179712000, 49109112520179712000, 23610150250086400, 5863137280, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
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.
EXAMPLE
The triangle begins as:
1;
1, 1;
1, 2, 1;
1, 16, 16, 1;
1, 416, 3328, 416, 1;
1, 33280, 6922240, 6922240, 33280, 1;
1, 8053760, 134014566400, 3484378726400, 134014566400, 8053760, 1;
MATHEMATICA
c[n_, q_]:= Product[(q^m-1)^(n-m), {m, 1, n}];
T[n_, k_, q_]:= c[n, q]/(c[k, q]*c[n-k, q]);
Table[T[n, k, 3], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 25 2021 *)
PROG
(Sage)
@CachedFunction
def c(n, q): return product( (q^j -1)^(n-j) for j in (1..n))
def T(n, k, q): return c(n, q)/(c(k, q)*c(n-k, q))
flatten([[T(n, k, 3) for k in (0..n)] for n in (0..10)]) # G. C. Greubel, Apr 25 2021
CROSSREFS
Sequence in context: A296524 A303935 A156697 * A322621 A309036 A294756
KEYWORD
nonn,tabl,less
AUTHOR
Roger L. Bagula, Feb 20 2010
EXTENSIONS
Edited by G. C. Greubel, Apr 25 2021
STATUS
approved

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Last modified March 28 07:32 EDT 2024. Contains 371235 sequences. (Running on oeis4.)