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 A318402 Number of sets of nonempty sets whose multiset union is a strongly normal multiset of size n. 3
 1, 2, 6, 20, 74, 311, 1401, 6913, 36376, 205421, 1228288, 7786802, 51937607, 364250763, 2673314121, 20504809133, 163844631872, 1361874185139, 11748149246269, 105029750531640, 971403871953460, 9282643841237360, 91519776792040324, 929892817423282068, 9725646244888190337 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..50 EXAMPLE The a(4) = 20 sets of sets:   {{1,2,3,4}}   {{1},{1,2,3}}   {{1},{2,3,4}}   {{2},{1,3,4}}   {{3},{1,2,4}}   {{4},{1,2,3}}   {{1,2},{1,3}}   {{1,2},{3,4}}   {{1,3},{2,4}}   {{1,4},{2,3}}   {{1},{2},{1,2}}   {{1},{2},{1,3}}   {{1},{2},{3,4}}   {{1},{3},{1,2}}   {{1},{3},{2,4}}   {{1},{4},{2,3}}   {{2},{3},{1,4}}   {{2},{4},{1,3}}   {{3},{4},{1,2}}   {{1},{2},{3},{4}} PROG (PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)} D(p, n)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); my(u=WeighT(v)); Vec(1/prod(k=1, n, 1 - u[k]*x^k + O(x*x^n))-1, -n)/prod(i=1, #v, i^v[i]*v[i]!)} seq(n)={my(s); for(k=1, n, forpart(p=k, s+=(-1)^(k+#p)*D(p, n))); s[n]+=1; s/2} \\ Andrew Howroyd, Dec 30 2020 CROSSREFS Cf. A007716, A049311, A050326, A116540, A283877, A292432, A292444, A318361, A318369, A318370. Sequence in context: A150158 A034010 A135588 * A293492 A150159 A150160 Adjacent sequences:  A318399 A318400 A318401 * A318403 A318404 A318405 KEYWORD nonn AUTHOR Gus Wiseman, Aug 25 2018 EXTENSIONS Terms a(10) and beyond from Andrew Howroyd, Dec 30 2020 STATUS approved

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Last modified July 29 08:13 EDT 2021. Contains 346340 sequences. (Running on oeis4.)