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 A347586 #7 Sep 08 2021 08:00:56
%S A347586 1,1,1,2,2,3,4,5,6,8,10,12,15,18,22,26,31,36,43,49,57,65,75,84,96,107,
%T A347586 121,134,150,165,184,201,222,242,266,288,315,340,370,398,431,462,499,
%U A347586 533,573,611,655,696,744,789,841,890,946,999,1060,1117,1182,1244,1314,1380,1455
%N A347586 Number of partitions of n into at most 4 distinct parts.
%H A347586 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-2,0,0,1,1,-1).
%F A347586 G.f.: Sum_{k=0..4} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).
%F A347586 a(n) ~ A000578(n)/144. - _Stefano Spezia_, Sep 08 2021
%t A347586 nmax = 60; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 0, 4}], {x, 0, nmax}], x]
%t A347586 Join[{1}, LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 8, 10}, 60]]
%Y A347586 Cf. A000578, A001400, A014591, A065033, A347587, A347588.
%K A347586 nonn,easy
%O A347586 0,4
%A A347586 _Ilya Gutkovskiy_, Sep 08 2021