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 A219561 #19 Sep 16 2019 04:29:18
%S A219561 1,15,457,14595,407287,10200931,233051939,4909342744,96272310302,
%T A219561 1771597038279,30795582025352,508466832109216,8011287089600483,
%U A219561 120926718707154007,1754672912487450236,24547188914867491083,331937179344717327559,4348524173437743243649,55300773426746984710983
%N A219561 Number of 4-partite partitions of (n,n,n,n) into distinct quadruples.
%C A219561 Number of factorizations of (p*q*r*s)^n into distinct factors where p, q, r, s are distinct primes.
%F A219561 a(n) = [(w*x*y*z)^n] 1/2 * Product_{i,j,k,m>=0} (1+w^i*x^j*y^k*z^m).
%e A219561 a(0) = 1: [].
%e A219561 a(1) = 15: [(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1)], [(0,0,1,1),(1,0,0,0),(0,1,0,0)], [(0,1,0,1),(1,0,0,0),(0,0,1,0)], [(0,1,1,0),(1,0,0,0),(0,0,0,1)], [(1,0,0,1),(0,1,0,0),(0,0,1,0)], [(1,0,0,1),(0,1,1,0)], [(1,0,1,0),(0,1,0,0),(0,0,0,1)], [(1,0,1,0),(0,1,0,1)], [(1,1,0,0),(0,0,1,0),(0,0,0,1)], [(1,1,0,0),(0,0,1,1)], [(0,1,1,1),(1,0,0,0)], [(1,0,1,1),(0,1,0,0)], [(1,1,0,1),(0,0,1,0)], [(1,1,1,0),(0,0,0,1)], [(1,1,1,1)].
%t A219561 a[n_] := If[n == 0, 1, (1/2) Coefficient[Product[O[w]^(n+1) + O[x]^(n+1) + O[y]^(n+1) + O[z]^(n+1) + (1 + w^i x^j y^k z^m), {i, 0, n}, {j, 0, n}, {k, 0, n}, {m, 0, n}] // Normal, (w x y z)^n]];
%t A219561 Table[Print[n]; a[n], {n, 0, 12}] (* _Jean-François Alcover_, Sep 16 2019 *)
%Y A219561 Column k=4 of A219585.
%Y A219561 Cf. A002774, A219554, A219560, A219565.
%K A219561 nonn
%O A219561 0,2
%A A219561 _Alois P. Heinz_, Nov 23 2012
%E A219561 a(9) from _Alois P. Heinz_, Oct 15 2014
%E A219561 a(10)-a(18) from _Andrew Howroyd_, Dec 17 2018