OFFSET
0,2
COMMENTS
In a multiset partition, two vertices are equivalent if in every block the multiplicity of the first is equal to the multiplicity of the second. a(n) is the number of non-isomorphic multiset partitions of {1, 1, 2, 2, 3, 3, ..., n, n} with no equivalent vertices. For example, non-isomorphic representatives of the a(2) = 5 multiset partitions are (1)(122), (11)(22), (1)(1)(22), (1)(2)(12), (1)(1)(2)(2). - Gus Wiseman, Jul 18 2018
a(n) is the number of unlabeled simple graphs with n edges rooted at one vertex. - Andrew Howroyd, Nov 22 2020
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
FORMULA
Euler transform of A191970. - Andrew Howroyd, Oct 22 2019
MATHEMATICA
seq[n_] := Module[{A = O[x]^n}, G[2n, x+A, {1}] // CoefficientList[#, x]&]; (* Jean-François Alcover, Dec 03 2020, using Andrew Howroyd's code for g.f. G in A339063 *)
PROG
(PARI) \\ See A339063 for G.
seq(n)={my(A=O(x*x^n)); Vec(G(2*n, x+A, [1]))} \\ Andrew Howroyd, Nov 22 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Jan 10 2000
EXTENSIONS
a(16)-a(24) from Max Alekseyev, Jan 22 2010
Terms a(25) and beyond from Andrew Howroyd, Oct 22 2019
STATUS
approved