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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
OFFSET
1,2
COMMENTS
A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities.
LINKS
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 25 2018
EXTENSIONS
Terms a(10) and beyond from Andrew Howroyd, Dec 30 2020
STATUS
approved