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 A221142 #17 Aug 08 2021 01:56:12
%S A221142 0,0,0,1,9,45,166,505,1341,3223,7149,14916,29480,55902,101892,180245,
%T A221142 309297,518859,849563,1366441,2154789,3348972,5119981,7733835,
%U A221142 11520100,16985374,24746334,35735413,51073008,72432093,101794713,142085314,196744665,270764547
%N A221142 Fourth-order spt function.
%H A221142 F. G. Garvan, <a href="http://qseries.org/fgarvan/papers/hspt.pdf">Higher-order spt functions</a>, preprint.
%H A221142 F. G. Garvan, <a href="https://arxiv.org/abs/1008.1207">Higher-order spt functions</a>, arXiv:1008.1207 [math.NT], 2010.
%H A221142 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 A221142 om[4, p_List] := Module[{pu, m, f}, pu = Union[p]; m = Length[pu]; f[j_] := Count[p, pu[[j]]]; Binomial[f[1] + 3, 7] + Binomial[f[1] + 2, 5] Sum[Binomial[f[j] + 1, 2], {j, 2, m}] + Binomial[f[1] + 1, 3] Sum[Binomial[f[j] + 2, 4], {j, 2, m}] + f[1] Sum[Binomial[f[j] + 3, 6], {j, 2, m}] + Binomial[f[1] + 1, 3] Sum[Binomial[f[j] + 1, 2] Binomial[f[k] + 1, 2], {j, 2, m}, {k, j + 1, m}] + f[1] Sum[Binomial[f[j] + 2, 4] Binomial[f[k] + 1, 2], {j, 2, m}, {k, j + 1, m}] + f[1] Sum[Binomial[f[j] + 1, 2] Binomial[f[k] + 2, 4], {j, 2, m}, {k, j + 1, m}] + f[1] Sum[Binomial[f[j] + 1, 2] Binomial[f[k] + 1, 2] Binomial[f[r] + 1, 2], {j, 2, m}, {k, j + 1, m}, {r, k + 1, m}]];
%t A221142 spt[4, n_] := Sum[om[4, p], {p, IntegerPartitions[n]}];
%t A221142 Table[spt[4, n], {n, 1, 35}] (* _Jinyuan Wang_, Aug 08 2021 *)
%Y A221142 Cf. A092269, A221140, A221141, A221143, A221144.
%K A221142 nonn
%O A221142 1,5
%A A221142 _N. J. A. Sloane_, Jan 02 2013
%E A221142 More terms from _Jinyuan Wang_, Aug 08 2021