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 A320395 Number of non-isomorphic 3-uniform multiset systems over {1,...,n}. 8
 1, 2, 10, 208, 45960, 287800704, 100103176111616, 3837878984050795692032, 32966965900633495618246298767360, 128880214965936601447070466061615999984402432, 464339910355487357558396669850788946402420533504952464572416 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..25 EXAMPLE Non-isomorphic representatives of the a(2) = 10 multiset systems:   {}   {{111}}   {{122}}   {{111}{222}}   {{112}{122}}   {{112}{222}}   {{122}{222}}   {{111}{122}{222}}   {{112}{122}{222}}   {{111}{112}{122}{222}} MATHEMATICA Table[Sum[2^PermutationCycles[Ordering[Map[Sort, Select[Tuples[Range[n], 3], OrderedQ]/.Rule@@@Table[{i, prm[[i]]}, {i, n}], {1}]], Length], {prm, Permutations[Range[n]]}]/n!, {n, 6}] PROG (PARI) 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} rep(typ)={my(L=List(), k=0); for(i=1, #typ, k+=typ[i]; listput(L, k); while(#L0, u=vecsort(apply(f, u)); d=lex(u, v)); !d} Q(perm)={my(t=0); forsubset([#perm+2, 3], v, t += can([v[1], v[2]-1, v[3]-2], t->perm[t])); t} a(n)={my(s=0); forpart(p=n, s += permcount(p)*2^Q(rep(p))); s/n!} \\ Andrew Howroyd, Aug 26 2019 CROSSREFS The 2-uniform case is A000666. The case of sets (as opposed to multisets) is A000665. The case of labeled spanning sets is A302374, with unlabeled case A322451. Cf. A000088, A000612, A003180, A070166, A301922, A317795, A319876. Sequence in context: A246532 A159558 A297066 * A001528 A293148 A193482 Adjacent sequences:  A320392 A320393 A320394 * A320396 A320397 A320398 KEYWORD nonn AUTHOR Gus Wiseman, Dec 12 2018 EXTENSIONS Terms a(9) and beyond from Andrew Howroyd, Aug 26 2019 STATUS approved

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Last modified June 25 16:08 EDT 2022. Contains 354851 sequences. (Running on oeis4.)