OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(4) = 13 multiset partitions:
{{1}} {{1,2}} {{1},{2,3}} {{1,2},{1,2}}
{{1},{1}} {{2},{1,2}} {{1,2},{3,4}}
{{1},{2}} {{1},{1},{1}} {{1,3},{2,3}}
{{1},{2},{2}} {{1},{1},{2,3}}
{{1},{2},{3}} {{1},{2},{1,2}}
{{1},{2},{3,4}}
{{1},{3},{2,3}}
{{2},{2},{1,2}}
{{1},{1},{1},{1}}
{{1},{1},{2},{2}}
{{1},{2},{2},{2}}
{{1},{2},{3},{3}}
{{1},{2},{3},{4}}
PROG
(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
gs(v) = {sum(i=2, #v, sum(j=1, i-1, my(g=gcd(v[i], v[j])); g*x^(2*v[i]*v[j]/g))) + sum(i=1, #v, my(r=v[i]); (1 + (1+r)%2)*x^r + ((r-1)\2)*x^(2*r))}
a(n)={if(n==0, 1, my(s=0); forpart(p=n, s+=permcount(p)*EulerT(Vec(gs(p) + O(x*x^n), -n))[n]); s/n!)} \\ Andrew Howroyd, Apr 16 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 09 2021
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Apr 16 2021
STATUS
approved