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A320291
Number of singleton-free multiset partitions of integer partitions of n with no 1's.
1
1, 0, 0, 0, 1, 1, 3, 3, 7, 8, 15, 19, 36, 46, 79, 110, 181, 254, 407, 580, 907, 1309, 2004, 2909, 4410, 6407, 9599, 13984, 20782, 30252, 44677, 64967, 95414, 138563, 202527, 293583, 427442, 618337, 897023, 1295020, 1872696, 2697777, 3889964, 5591917, 8041593, 11535890
OFFSET
0,7
LINKS
FORMULA
Euler transform of A083751. - Andrew Howroyd, Oct 25 2018
EXAMPLE
The a(4) = 1 through a(10) = 15 multiset partitions:
((22)) ((23)) ((24)) ((25)) ((26)) ((27)) ((28))
((33)) ((34)) ((35)) ((36)) ((37))
((222)) ((223)) ((44)) ((45)) ((46))
((224)) ((225)) ((55))
((233)) ((234)) ((226))
((2222)) ((333)) ((235))
((22)(22)) ((2223)) ((244))
((22)(23)) ((334))
((2224))
((2233))
((22222))
((22)(24))
((22)(33))
((23)(23))
((22)(222))
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]]]];
Table[Length[Select[Join@@mps/@Select[IntegerPartitions[n], FreeQ[#, 1]&], FreeQ[Length/@#, 1]&]], {n, 20}]
PROG
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(v=vector(n, i, i>1)); concat([1], EulerT(EulerT(v)-v))} \\ Andrew Howroyd, Oct 25 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 09 2018
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Oct 25 2018
STATUS
approved