OFFSET
0,3
COMMENTS
The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
An endpoint is a vertex appearing only once (degree 1).
Also the number of non-isomorphic multiset partitions of weight n with at least one singleton.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
Wikipedia, Degree (graph theory)
FORMULA
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 21 multiset partitions:
{1} {12} {122} {1222}
{1}{2} {123} {1233}
{1}{22} {1234}
{1}{23} {1}{222}
{2}{12} {12}{22}
{1}{2}{2} {1}{233}
{1}{2}{3} {12}{33}
{1}{234}
{12}{34}
{13}{23}
{2}{122}
{3}{123}
{1}{1}{23}
{1}{2}{22}
{1}{2}{33}
{1}{2}{34}
{1}{3}{23}
{2}{2}{12}
{1}{2}{2}{2}
{1}{2}{3}{3}
{1}{2}{3}{4}
CROSSREFS
The complement is counted by A302545.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 30 2019
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Jan 15 2023
STATUS
approved