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 A281615 #7 Sep 15 2021 06:01:06
%S A281615 1,2,4,6,8,13,17,21,30,37,44,60,72,83,107,127,144,181,210,236,289,333,
%T A281615 371,446,507,562,664,750,825,965,1083,1187,1371,1530,1668,1912,2122,
%U A281615 2307,2618,2896,3138,3540,3897,4211,4717,5180,5581,6222,6803,7317,8116,8853,9497,10486,11401,12215,13430,14572,15576,17067
%N A281615 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 A281615 Total number of parts in all partitions of n into nonzero triangular numbers (A000217).
%C A281615 Convolution of A007294 and A007862.
%H A281615 Vaclav Kotesovec, <a href="/A281615/b281615.txt">Table of n, a(n) for n = 1..10000</a>
%H A281615 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A281615 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)).
%F A281615 a(n) ~ exp(3*zeta(3/2)^(2/3) * (Pi*n)^(1/3)/2) * zeta(3/2)^(1/3) / (2^(3/2) * sqrt(3) * Pi^(4/3) * n^(5/6)). - _Vaclav Kotesovec_, Sep 15 2021
%e A281615 a(6) = 13 because we have [6], [3, 3], [3, 1, 1, 1], [1, 1, 1, 1, 1, 1] and 1 + 2 + 4 + 6 = 13.
%t A281615 nmax = 60; 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 A281615 Cf. A000217, A007294, A007862, A281541.
%K A281615 nonn
%O A281615 1,2
%A A281615 _Ilya Gutkovskiy_, Jan 25 2017