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 A316222 #4 Jun 27 2018 13:15:52 %S A316222 1,5,20,74,258,855,2736,8447 %N A316222 Number of positive subset-sum triangles whose composite is a positive subset-sum of an integer partition of n. %C A316222 A positive subset-sum is a pair (h,g), where h is a positive integer and g is an integer partition, such that some submultiset of g sums to h. A triangle consists of a root sum r and a sequence of positive subset-sums ((h_1,g_1),...,(h_k,g_k)) such that the sequence (h_1,...,h_k) is weakly decreasing and has a submultiset summing to r. %e A316222 We write positive subset-sum triangles in the form rootsum(branch,...,branch). The a(2) = 5 positive subset-sum triangles: %e A316222 2(2(2)) %e A316222 1(1(1,1)) %e A316222 2(2(1,1)) %e A316222 1(1(1),1(1)) %e A316222 2(1(1),1(1)) %Y A316222 Cf. A063834, A262671, A269134, A276024, A281113, A301934, A301935, A316219, A316220. %K A316222 nonn,more %O A316222 1,2 %A A316222 _Gus Wiseman_, Jun 27 2018