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A173504
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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.
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2
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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
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OFFSET
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0,5
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LINKS
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FORMULA
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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.
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EXAMPLE
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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;
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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