cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A173504 #8 Apr 26 2021 01:54:43
%S A173504 1,1,1,1,2,1,1,16,16,1,1,416,3328,416,1,1,33280,6922240,6922240,33280,
%T A173504 1,1,8053760,134014566400,3484378726400,134014566400,8053760,1,1,
%U A173504 5863137280,23610150250086400,49109112520179712000,49109112520179712000,23610150250086400,5863137280,1
%N 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.
%H A173504 G. C. Greubel, <a href="/A173504/b173504.txt">Rows n = 0..23 of the triangle, flattened</a>
%F A173504 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 A173504 The triangle begins as:
%e A173504   1;
%e A173504   1,       1;
%e A173504   1,       2,            1;
%e A173504   1,      16,           16,             1;
%e A173504   1,     416,         3328,           416,            1;
%e A173504   1,   33280,      6922240,       6922240,        33280,       1;
%e A173504   1, 8053760, 134014566400, 3484378726400, 134014566400, 8053760, 1;
%t A173504 c[n_, q_]:= Product[(q^m-1)^(n-m), {m,1,n}];
%t A173504 T[n_, k_, q_]:= c[n, q]/(c[k, q]*c[n-k, q]);
%t A173504 Table[T[n, k, 3], {n,0,10}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Apr 25 2021 *)
%o A173504 (Sage)
%o A173504 @CachedFunction
%o A173504 def c(n,q): return product( (q^j -1)^(n-j) for j in (1..n))
%o A173504 def T(n,k,q): return c(n,q)/(c(k,q)*c(n-k,q))
%o A173504 flatten([[T(n,k,3) for k in (0..n)] for n in (0..10)]) # _G. C. Greubel_, Apr 25 2021
%Y A173504 Cf. A173503, A173505.
%K A173504 nonn,tabl,less
%O A173504 0,5
%A A173504 _Roger L. Bagula_, Feb 20 2010
%E A173504 Edited by _G. C. Greubel_, Apr 25 2021