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 A302831 #9 Apr 14 2018 15:22:40
%S A302831 1,2,4,9,16,31,56,99,163,283,469,757,1220,1915,3020,4748,7273,11014,
%T A302831 16789,25033,37480,55782,82206,120033,174762,253092,364276,523814,
%U A302831 749438,1064853,1509561,2128227,2986392,4186093,5832169,8121130,11272081,15576076,21446615,29479186,40360980
%N A302831 Expansion of (1/(1 - x))*Product_{k>=1} (1 + k*x^k).
%C A302831 Partial sums of A022629.
%H A302831 Alois P. Heinz, <a href="/A302831/b302831.txt">Table of n, a(n) for n = 0..10000</a>
%H A302831 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A302831 G.f.: (1/(1 - x))*exp(Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j).
%p A302831 b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
%p A302831 `if`(n=0, 1, b(n, i-1)+`if`(i>n, 0, i*b(n-i, i-1))))
%p A302831 end:
%p A302831 a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+b(n$2)) end:
%p A302831 seq(a(n), n=0..40); # _Alois P. Heinz_, Apr 13 2018
%t A302831 nmax = 40; CoefficientList[Series[1/(1 - x) Product[(1 + k x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A302831 nmax = 40; CoefficientList[Series[1/(1 - x) Exp[Sum[Sum[(-1)^(j + 1) k^j x^(j k)/j, {k, 1, nmax}], {j, 1, nmax}]], {x, 0, nmax}], x]
%Y A302831 Cf. A000009, A022629, A036469, A302830, A302832.
%K A302831 nonn
%O A302831 0,2
%A A302831 _Ilya Gutkovskiy_, Apr 13 2018