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 A281666 #8 Sep 15 2021 03:23:37
%S A281666 1,0,1,2,0,1,2,0,2,4,2,0,2,3,1,4,3,2,6,4,3,5,0,5,9,3,2,7,6,3,11,10,0,
%T A281666 9,12,3,11,10,8,11,8,9,9,6,12,19,15,7,15,16,4,20,21,10,23,24,10,16,19,
%U A281666 18,20,20,17,24,27,18,28,26,19,33,30,12,33,39,25,36,38,16,32,44,29,41,48,37,41,45,33,39,44,41
%N A281666 Expansion of Sum_{i>=1} x^(i*(i+1)/2)/(1 + x^(i*(i+1)/2)) * Product_{j>=1} (1 + x^(j*(j+1)/2)).
%C A281666 Total number of parts in all partitions of n into distinct nonzero triangular numbers (A000217).
%H A281666 Vaclav Kotesovec, <a href="/A281666/b281666.txt">Table of n, a(n) for n = 1..10000</a>
%H A281666 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A281666 G.f.: Sum_{i>=1} x^(i*(i+1)/2)/(1 + x^(i*(i+1)/2)) * Product_{j>=1} (1 + x^(j*(j+1)/2)).
%e A281666 a(10) = 4 because we have [10], [6, 3, 1] and 1 + 3 = 4.
%t A281666 nmax = 90; Rest[CoefficientList[Series[Sum[x^(i (i + 1)/2)/(1 + x^(i (i + 1)/2)), {i, 1, nmax}] Product[1 + x^(j (j + 1)/2), {j, 1, nmax}], {x, 0, nmax}], x]]
%Y A281666 Cf. A000217, A015723, A024940, A281542, A281615, A329801.
%K A281666 nonn
%O A281666 1,4
%A A281666 _Ilya Gutkovskiy_, Jan 26 2017