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 A323655 #8 Aug 26 2019 21:07:03
%S A323655 1,1,4,7,19,35,80,149,307,566,1092,1974,3643,6447,11498,19947,34636,
%T A323655 58974,100182,167713,279659,461056,756562,1230104,1990255,3195471,
%U A323655 5105540,8103722,12801925,20107448,31439978,48907179,75755094,116797754,179354540,274253042
%N A323655 Number of non-isomorphic multiset partitions of weight n with at most 2 distinct vertices, or with at most 2 (not necessarily distinct) edges.
%C A323655 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%C A323655 Also the number of nonnegative integer matrices with only one or two columns, no zero rows or columns, and sum of entries equal to n, up to row and column permutations.
%H A323655 Andrew Howroyd, <a href="/A323655/b323655.txt">Table of n, a(n) for n = 0..1000</a>
%F A323655 a(2*n) = (A005380(2*n) + A005986(n))/2; a(2*n+1) = A005380(2*n+1)/2. - _Andrew Howroyd_, Aug 26 2019
%e A323655 Non-isomorphic representatives of the a(1) = 1 through a(4) = 19 multiset partitions with at most 2 distinct vertices:
%e A323655 {{1}} {{11}} {{111}} {{1111}}
%e A323655 {{12}} {{122}} {{1122}}
%e A323655 {{1}{1}} {{1}{11}} {{1222}}
%e A323655 {{1}{2}} {{1}{22}} {{1}{111}}
%e A323655 {{2}{12}} {{11}{11}}
%e A323655 {{1}{1}{1}} {{1}{122}}
%e A323655 {{1}{2}{2}} {{11}{22}}
%e A323655 {{12}{12}}
%e A323655 {{1}{222}}
%e A323655 {{12}{22}}
%e A323655 {{2}{122}}
%e A323655 {{1}{1}{11}}
%e A323655 {{1}{1}{22}}
%e A323655 {{1}{2}{12}}
%e A323655 {{1}{2}{22}}
%e A323655 {{2}{2}{12}}
%e A323655 {{1}{1}{1}{1}}
%e A323655 {{1}{1}{2}{2}}
%e A323655 {{1}{2}{2}{2}}
%e A323655 Non-isomorphic representatives of the a(1) = 1 through a(4) = 19 multiset partitions with at most 2 edges:
%e A323655 {{1}} {{11}} {{111}} {{1111}}
%e A323655 {{12}} {{122}} {{1122}}
%e A323655 {{1}{1}} {{123}} {{1222}}
%e A323655 {{1}{2}} {{1}{11}} {{1233}}
%e A323655 {{1}{22}} {{1234}}
%e A323655 {{1}{23}} {{1}{111}}
%e A323655 {{2}{12}} {{11}{11}}
%e A323655 {{1}{122}}
%e A323655 {{11}{22}}
%e A323655 {{12}{12}}
%e A323655 {{1}{222}}
%e A323655 {{12}{22}}
%e A323655 {{1}{233}}
%e A323655 {{12}{33}}
%e A323655 {{1}{234}}
%e A323655 {{12}{34}}
%e A323655 {{13}{23}}
%e A323655 {{2}{122}}
%e A323655 {{3}{123}}
%e A323655 Inequivalent representatives of the a(4) = 19 matrices:
%e A323655 [4] [2 2] [1 3]
%e A323655 .
%e A323655 [1] [1 0] [1 0] [0 1] [2] [2 0] [1 1] [1 1]
%e A323655 [3] [1 2] [0 3] [1 2] [2] [0 2] [1 1] [0 2]
%e A323655 .
%e A323655 [1] [1 0] [1 0] [1 0] [0 1]
%e A323655 [1] [1 0] [0 1] [0 1] [0 1]
%e A323655 [2] [0 2] [1 1] [0 2] [1 1]
%e A323655 .
%e A323655 [1] [1 0] [1 0]
%e A323655 [1] [1 0] [0 1]
%e A323655 [1] [0 1] [0 1]
%e A323655 [1] [0 1] [0 1]
%o A323655 (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A323655 seq(n)={concat(1, (EulerT(vector(n, k, k+1)) + EulerT(vector(n, k, if(k%2, 0, (k+6)\4))))/2)} \\ _Andrew Howroyd_, Aug 26 2019
%Y A323655 Cf. A007716, A052847, A005380, A054974, A005986, A120733, A316980, A323654, A323655, A323656.
%K A323655 nonn
%O A323655 0,3
%A A323655 _Gus Wiseman_, Jan 22 2019
%E A323655 Terms a(11) and beyond from _Andrew Howroyd_, Aug 26 2019