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 A317752 Number of multiset partitions of normal multisets of size n such that the blocks have empty intersection. 22
 0, 1, 8, 49, 305, 1984, 13686, 100124, 776885, 6386677, 55532358, 509549386, 4921352952, 49899820572, 529807799836, 5876162077537, 67928460444139, 816764249684450, 10195486840926032, 131896905499007474, 1765587483656124106, 24419774819813602870 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A multiset is normal if it spans an initial interval of positive integers. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 EXAMPLE The a(3) = 8 multiset partitions with empty intersection: {{2},{1,1}} {{1},{2,2}} {{1},{2,3}} {{2},{1,3}} {{3},{1,2}} {{1},{1},{2}} {{1},{2},{2}} {{1},{2},{3}} MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]]; allnorm[n_]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]; Table[Length[Join@@Table[Select[mps[m], Intersection@@#=={}&], {m, allnorm[n]}]], {n, 6}] PROG (PARI) P(n, k)={1/prod(i=1, n, (1 - x^i*y + O(x*x^n))^binomial(k+i-1, k-1))} R(n, k)={my(p=P(n, k), q=p/(1-y+O(y*y^n))); Vec(sum(i=2, n, polcoef(p, i, y) + polcoef(q, i, y)*sum(j=1, n\i, (-1)^j*binomial(k, j)*x^(i*j))), -n)} seq(n)={sum(k=2, n, R(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)) )} \\ Andrew Howroyd, Feb 05 2021 CROSSREFS Cf. A007716, A255903, A255906, A317073, A281116, A317077, A317532, A317533. Cf. A317748, A317751, A317755, A317757, A317776. Sequence in context: A037539 A037483 A188708 * A273497 A024106 A176626 Adjacent sequences: A317749 A317750 A317751 * A317753 A317754 A317755 KEYWORD nonn AUTHOR Gus Wiseman, Aug 06 2018 EXTENSIONS Terms a(9) and beyond from Andrew Howroyd, Feb 05 2021 STATUS approved

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Last modified May 29 15:14 EDT 2023. Contains 363042 sequences. (Running on oeis4.)