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 A221140 #26 Apr 01 2020 00:35:31
%S A221140 0,1,5,15,35,75,140,259,435,735,1155,1841,2765,4200,6125,8975,12731,
%T A221140 18179,25235,35180,48055,65681,88299,118895,157690,209230,274510,
%U A221140 359779,466970,605740,778860,1000462,1276044,1624845,2056355,2598855,3265851,4097763,5117350
%N A221140 Second-order spt function.
%H A221140 Jean-François Alcover, <a href="/A221140/b221140.txt">Table of n, a(n) for n = 1..60</a>
%H A221140 F. G. Garvan, <a href="http://qseries.org/fgarvan/papers/hspt.pdf">Higher-order spt functions</a>, preprint.
%H A221140 F. G. Garvan, <a href="https://arxiv.org/abs/1008.1207">Higher-order spt functions</a>, arXiv:1008.1207 [math.NT], 2010.
%H A221140 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 A221140 om[2, p_List] := Module[{pu, m, f}, pu = Union[p]; m = Length[pu]; f[j_] := Count[p, pu[[j]]]; Binomial[f[1] + 1, 3] + f[1] Sum[Binomial[f[j] + 1, 2], {j, 2, m}]];
%t A221140 spt[2, n_] := Sum[om[2, p], {p, IntegerPartitions[n]}];
%t A221140 Table[spt[2, n], {n, 1, 29}] (* _Jean-François Alcover_, Mar 30 2020 *)
%Y A221140 Cf. A092269, A221141, A221142, A221143, A221144.
%K A221140 nonn
%O A221140 1,3
%A A221140 _N. J. A. Sloane_, Jan 02 2013
%E A221140 More terms from _Jean-François Alcover_, Mar 30 2020