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 A014160 #34 Mar 20 2023 17:37:47
%S A014160 1,4,11,25,51,96,171,291,478,762,1185,1803,2693,3956,5727,8182,11552,
%T A014160 16134,22313,30579,41559,56045,75039,99796,131891,173282,226405,
%U A014160 294270,380595,489945,627924,801374,1018644
%N A014160 Apply partial sum operator thrice to partition numbers.
%C A014160 A014160 convolved with A010815 = A000217, the triangular numbers. - _Gary W. Adamson_, Nov 09 2008
%C A014160 Unordered partitions of n into parts where the part 1 comes in 4 colors. - _Peter Bala_, Dec 23 2013
%C A014160 From _Omar E. Pol_, Mar 01 2023: (Start)
%C A014160 Partial sums of A014153.
%C A014160 Convolution of A000070 and A000027.
%C A014160 Convolution of A000041 and the positive terms of A000217.
%C A014160 Convolution of A002865 and the positive terms of A000292. (End)
%H A014160 Vaclav Kotesovec, <a href="/A014160/b014160.txt">Table of n, a(n) for n = 0..10000</a>
%F A014160 From _Peter Bala_, Dec 23 2013: (Start)
%F A014160 O.g.f.: 1/(1 - x)^3 * Product_{k >= 1} 1/(1 - x^k).
%F A014160 a(n-1) + a(n-2) = Sum_{parts k in all partitions of n} J_2(k), where J_2(n) is the Jordan totient function A007434(n). (End)
%F A014160 a(n) ~ 3*sqrt(n) * exp(Pi*sqrt(2*n/3)) / (sqrt(2)*Pi^3). - _Vaclav Kotesovec_, Oct 30 2015
%F A014160 a(n) = Sum_{k=0..n} A014153(k). - _Sean A. Irvine_, Oct 14 2018
%t A014160 nmax = 50; CoefficientList[Series[1/((1-x)^3 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 30 2015 *)
%Y A014160 Cf. A000041, A000070, A014153.
%Y A014160 Cf. A010815, A000217. - _Gary W. Adamson_, Nov 09 2008
%Y A014160 Column k=4 of A292508.
%Y A014160 Cf. A000027, A002865, A000292.
%K A014160 nonn
%O A014160 0,2
%A A014160 _N. J. A. Sloane_