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A173505
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 = 4, read by rows.
3
1, 1, 1, 1, 3, 1, 1, 45, 45, 1, 1, 2835, 42525, 2835, 1, 1, 722925, 683164125, 683164125, 722925, 1, 1, 739552275, 178213609468125, 11227457396491875, 178213609468125, 739552275, 1, 1, 3028466566125, 746569779579727228125, 11993643508948317919828125, 11993643508948317919828125, 746569779579727228125, 3028466566125, 1
OFFSET
0,5
FORMULA
q=4;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))
EXAMPLE
The triangle begins as:
1;
1, 1;
1, 3, 1;
1, 45, 45, 1;
1, 2835, 42525, 2835, 1;
1, 722925, 683164125, 683164125, 722925, 1;
1, 739552275, 178213609468125, 11227457396491875, 178213609468125, 739552275, 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, 4], {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, 4) for k in (0..n)] for n in (0..10)]) # G. C. Greubel, Apr 25 2021
CROSSREFS
Sequence in context: A156698 A083993 A156727 * A253178 A174587 A177848
KEYWORD
nonn,tabl,less
AUTHOR
Roger L. Bagula, Feb 20 2010
EXTENSIONS
Edited by G. C. Greubel, Apr 25 2021
STATUS
approved