OFFSET
0,3
COMMENTS
Number of sets of disjoint nonempty sets of nonempty multisets of positive integers with total sum n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
EXAMPLE
The a(4) = 13 partitions:
((4)) ((22)) ((31)) ((211)) ((1111))
((1)(3)) ((1)(21)) ((1)(111))
((1))((3)) ((2)(11)) ((1))((111))
((1))((21))
((2))((11))
MATHEMATICA
ppl[n_, k_]:=Switch[k, 0, {n}, 1, IntegerPartitions[n], _, Join@@Table[Union[Sort/@Tuples[ppl[#, k-1]&/@ptn]], {ptn, IntegerPartitions[n]}]];
Table[Length[Select[ppl[n, 3], UnsameQ@@Join@@#&]], {n, 0, 10}]
PROG
(PARI) \\ here BellP is A000110 as series.
BellP(n)={serlaplace(exp( exp(x + O(x*x^n)) - 1))}
seq(n)={my(b=BellP(n), v=Vec(prod(k=1, n, (1 + x^k*y + O(x*x^n))^numbpart(k)))); vector(#v, n, my(r=v[n]); sum(k=0, n-1, polcoeff(b, k)*polcoef(r, k)))} \\ Andrew Howroyd, Dec 29 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 16 2019
EXTENSIONS
Terms a(18) and beyond from Andrew Howroyd, Dec 29 2019
STATUS
approved