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 A300626 #29 Jan 01 2021 18:12:02
%S A300626 1,1,3,11,43,187,872,4375,23258,130485,767348,4710715,30070205,
%T A300626 198983975,1361361925,9607908808,69812787049,521377973359,
%U A300626 3996036977270,31389624598631,252408597286705,2075472033455894,17434190966525003,149476993511444023,1307022313790487959
%N A300626 Number of inequivalent colorings of free pure symmetric multifunctions (with empty expressions allowed) with n positions.
%C A300626 A free pure symmetric multifunction (with empty expressions allowed) f in EOME is either (case 1) a positive integer, or (case 2) a possibly empty expression of the form h[g_1, ..., g_k] where k >= 0, h is in EOME, each of the g_i for i = 1, ..., k is in EOME, and for i < j we have g_i <= g_j under a canonical total ordering of EOME, such as the Mathematica ordering of expressions.
%C A300626 Also the number of inequivalent colorings of orderless Mathematica expressions with n positions.
%e A300626 Inequivalent representatives of the a(3) = 11 colorings:
%e A300626 1[1,1] 1[2,2] 1[1,2] 1[2,3]
%e A300626 1[1[]] 1[2[]]
%e A300626 1[][1] 1[][2]
%e A300626 1[1][] 1[2][]
%e A300626 1[][][]
%o A300626 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A300626 cycleIndexSeries(n)={my(p=O(x)); for(n=1, n, p = x*sv(1) + x*p*sExp(p)); p}
%o A300626 InequivalentColoringsSeq(cycleIndexSeries(15)) \\ _Andrew Howroyd_, Dec 30 2020
%Y A300626 Row sums of A304485.
%Y A300626 Cf. A000612, A007716, A052893, A053492, A277996, A279944, A280000, A317652, A317655, A317656, A317676.
%K A300626 nonn
%O A300626 0,3
%A A300626 _Gus Wiseman_, Aug 17 2018
%E A300626 Terms a(8) and beyond from _Andrew Howroyd_, Dec 30 2020