cp's OEIS Frontend

A323786 Number of non-isomorphic weight-n multisets of multisets of non-singleton multisets.

%I A323786 #9 Jan 17 2023 12:36:52
%S A323786 1,0,2,3,19,39,200,615,2849,11174,52377,239269,1191090,6041975,
%T A323786 32275288,177797719,1017833092,6014562272,36717301665,230947360981,
%U A323786 1495562098099,9956230757240,68070158777759,477439197541792,3432259679880648,25267209686664449
%N A323786 Number of non-isomorphic weight-n multisets of multisets of non-singleton multisets.
%C A323786 All sets and multisets must be finite, and only the outermost may be empty.
%C A323786 The weight of an atom is 1, and the weight of a multiset is the sum of weights of its elements, counting multiplicity.
%e A323786 Non-isomorphic representatives of the a(4) = 19 multiset partitions:
%e A323786   {{1111}}      {{1112}}      {{1123}}      {{1234}}
%e A323786   {{11}{11}}    {{1122}}      {{11}{23}}    {{12}{34}}
%e A323786   {{11}}{{11}}  {{11}{12}}    {{12}{13}}    {{12}}{{34}}
%e A323786                 {{11}{22}}    {{11}}{{23}}
%e A323786                 {{12}{12}}    {{12}}{{13}}
%e A323786                 {{11}}{{12}}
%e A323786                 {{11}}{{22}}
%e A323786                 {{12}}{{12}}
%e A323786 Non-isomorphic representatives of the a(5) = 39 multiset partitions:
%e A323786   {{11111}}      {{11112}}      {{11123}}      {{11234}}      {{12345}}
%e A323786   {{11}{111}}    {{11122}}      {{11223}}      {{11}{234}}    {{12}{345}}
%e A323786   {{11}}{{111}}  {{11}{112}}    {{11}{123}}    {{12}{134}}    {{12}}{{345}}
%e A323786                  {{11}{122}}    {{11}{223}}    {{23}{114}}
%e A323786                  {{12}{111}}    {{12}{113}}    {{11}}{{234}}
%e A323786                  {{12}{112}}    {{12}{123}}    {{12}}{{134}}
%e A323786                  {{22}{111}}    {{13}{122}}    {{23}}{{114}}
%e A323786                  {{11}}{{112}}  {{23}{111}}
%e A323786                  {{11}}{{122}}  {{11}}{{123}}
%e A323786                  {{12}}{{111}}  {{11}}{{223}}
%e A323786                  {{12}}{{112}}  {{12}}{{113}}
%e A323786                  {{22}}{{111}}  {{12}}{{123}}
%e A323786                                 {{13}}{{122}}
%e A323786                                 {{23}}{{111}}
%o A323786 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A323786 seq(n)={my(A=symGroupSeries(n)); NumUnlabeledObjsSeq(sCartProd(sExp(A), sExp(sExp(A-x*sv(1)))))} \\ _Andrew Howroyd_, Jan 17 2023
%Y A323786 Cf. A007716, A302545, A306186, A317791, A318564, A318566.
%Y A323786 Cf. A323787, A323788, A323789, A323790, A323791, A323792, A323793, A323794.
%K A323786 nonn
%O A323786 0,3
%A A323786 _Gus Wiseman_, Jan 28 2019
%E A323786 Terms a(8) and beyond from _Andrew Howroyd_, Jan 17 2023