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 A221141 #25 Jun 04 2020 12:03:01
%S A221141 0,0,1,7,28,85,217,497,1036,2044,3787,6797,11648,19558,31703,50645,
%T A221141 78674,120932,181664,270600,395682,574329,820834,1166109,1634668,
%U A221141 2279242,3142903,4312063,5859616,7927745,10635129,14209328,18846744,24900807,32688145,42761047
%N A221141 Third-order spt function.
%H A221141 Jean-François Alcover, <a href="/A221141/b221141.txt">Table of n, a(n) for n = 1..50</a>
%H A221141 F. G. Garvan, <a href="http://qseries.org/fgarvan/papers/hspt.pdf">Higher-order spt functions</a>, preprint.
%H A221141 F. G. Garvan, <a href="https://arxiv.org/abs/1008.1207">Higher-order spt functions</a>, arXiv:1008.1207 [math.NT], 2010.
%H A221141 F. G. Garvan, <a href="https://doi.org/10.1016/j.aim.2011.05.013">Higher-order spt functions</a>, Adv. Math. 228 (2011), no. 1, 241-265.
%t A221141 om[3, p_List] := Module[{pu, m, f}, pu = Union[p]; m = Length[pu]; f[j_] := Count[p, pu[[j]]]; Binomial[f[1] + 2, 5] + Binomial[f[1] + 1, 3] Sum[ Binomial[f[j] + 1, 2], {j, 2, m}] + f[1] Sum[Binomial[f[j] + 2, 4], {j, 2, m}] + f[1] Sum[Binomial[f[j] + 1, 2] Binomial[f[k] + 1, 2], {j, 2, m}, {k, j + 1, m}]];
%t A221141 spt[3, n_] := Sum[om[3, p], {p, IntegerPartitions[n]}];
%t A221141 Table[spt[3, n], {n, 1, 29}] (* _Jean-François Alcover_, Mar 30 2020 *)
%Y A221141 Cf. A092269, A221140, A221142, A221143, A221144.
%K A221141 nonn
%O A221141 1,4
%A A221141 _N. J. A. Sloane_, Jan 02 2013
%E A221141 More terms from _Jean-François Alcover_, Mar 30 2020