OFFSET
0,3
COMMENTS
The number of non-isomorphic multiset partitions of weight n is A007716(n).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 12 multiset partitions:
{{1}} {{1,1}} {{1,1,1}} {{1,1,1,1}}
{{1,2}} {{1,2,2}} {{1,1,2,2}}
{{1,2,3}} {{1,2,2,2}}
{{1},{1,1}} {{1,2,3,3}}
{{1},{2,2}} {{1,2,3,4}}
{{1},{2,3}} {{1},{1,1,1}}
{{2},{1,2}} {{1},{1,2,2}}
{{1},{2,2,2}}
{{1},{2,3,3}}
{{1},{2,3,4}}
{{2},{1,2,2}}
{{3},{1,2,3}}
PROG
(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
D(p, n)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); my(u=EulerT(v)); polcoef(prod(k=1, #u, 1 + u[k]*x^k + O(x*x^n)), n)/prod(i=1, #v, i^v[i]*v[i]!)}
a(n)={my(s=0); forpart(p=n, s+=D(p, n)); s} \\ Andrew Howroyd, Feb 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 13 2019
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Feb 08 2020
STATUS
approved