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.
%I A238743 #19 Jan 25 2016 14:22:05
%S A238743 1,1,1,1,7,1,1,26,26,1,1,56,208,56,1,1,124,992,992,124,1,1,182,3224,
%T A238743 6944,3224,182,1,1,342,8892,42408,42408,8892,342,1,1,448,21888,153216,
%U A238743 339264,153216,21888,448,1,1,702,44928,590976,1920672,1920672,590976,44928
%N A238743 Triangle read by rows: T(n,k) = A059382(n)/(A059382(k)*A059382(n-k)).
%C A238743 We assume that A059382(0)=1 since it would be the empty product.
%C A238743 These are the generalized binomial coefficients associated with the Jordan totient function J_3 given in A059376.
%C A238743 Another name might be the 3-totienomial coefficients.
%H A238743 Tom Edgar, <a href="http://www.emis.de/journals/INTEGERS/papers/o62/o62.Abstract.html">Totienomial Coefficients</a>, INTEGERS, 14 (2014), #A62.
%H A238743 Tom Edgar and Michael Z. Spivey, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Edgar/edgar3.html">Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers</a>, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.
%H A238743 Donald E. Knuth and Herbert S. Wilf, <a href="http://www.math.upenn.edu/~wilf/website/dm36.pdf">The power of a prime that divides a generalized binomial coefficient</a>, J. Reine Angew. Math., 396:212-219, 1989.
%F A238743 T(n,k) = A059382(n)/(A059382(k)* A059382(n-k)).
%F A238743 T(n,k) = prod_{i=1..n} A059376(i)/(prod_{i=1..k} A059376(i)*prod_{i=1..n-k} A059376(i)).
%F A238743 T(n,k) = A059376(n)/n*(k/A059376(k)*T(n-1,k-1)+(n-k)/A059376(n-k)*T(n-1,k)).
%e A238743 The first five terms in the third Jordan totient function are 1,7,26,56,124 and so T(4,2) = 56*26*7*1/((7*1)*(7*1))=208 and T(5,3) = 124*56*26*7*1/((26*7*1)*(7*1))=992.
%e A238743 The triangle begins
%e A238743 1
%e A238743 1 1
%e A238743 1 7 1
%e A238743 1 26 26 1
%e A238743 1 56 208 56 1
%e A238743 1 124 992 992 124 1
%e A238743 1 182 3224 6944 3224 182 1
%o A238743 (Sage)
%o A238743 q=100 #change q for more rows
%o A238743 P=[0]+[i^3*prod([1-1/p^3 for p in prime_divisors(i)]) for i in [1..q]]
%o A238743 [[prod(P[1:n+1])/(prod(P[1:k+1])*prod(P[1:(n-k)+1])) for k in [0..n]] for n in [0..len(P)-1]] #generates the triangle up to q rows.
%Y A238743 Cf. A059382, A059376, A238688, A238453.
%K A238743 nonn,tabl
%O A238743 0,5
%A A238743 _Tom Edgar_, Mar 04 2014