OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..130
EXAMPLE
Non-isomorphic representatives of the a(12) = 9 multiset partitions of {1,1,2,3}:
{{1,1,2,3}}
{{1},{1,2,3}}
{{2},{1,1,3}}
{{1,1},{2,3}}
{{1,2},{1,3}}
{{1},{1},{2,3}}
{{1},{2},{1,3}}
{{2},{3},{1,1}}
{{1},{1},{2},{3}}
PROG
(PARI) \\ See links in A339645 for combinatorial species functions.
sig(n)={my(f=factor(n), sig=vector(primepi(vecmax(f[, 1])))); for(i=1, #f~, sig[primepi(f[i, 1])]=f[i, 2]); sig}
C(sig)={my(n=sum(i=1, #sig, i*sig[i]), A=Vec(symGroupSeries(n)-1), B=O(x*x^n), c=prod(i=1, #sig, if(sig[i], sApplyCI(A[sig[i]], sig[i], A[i], i), 1))); polcoef(OgfSeries(sCartProd(c*x^n + B, sExp(x*Ser(A) + B))), n)}
a(n)={if(n==1, 1, C(sig(n)))} \\ Andrew Howroyd, Jan 17 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 23 2018
EXTENSIONS
Terms a(31) and beyond from Andrew Howroyd, Jan 17 2023
STATUS
approved