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A279790
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Number of twice-partitions of type (Q,P,Q) and weight n.
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14
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1, 1, 3, 3, 5, 11, 12, 18, 24, 49, 53, 82, 102, 149, 236, 297, 392, 540, 702, 924, 1423, 1723, 2318, 3016, 3969, 5037, 6647, 9285, 11448, 15048, 19143, 24695, 31288, 40075, 50014, 68583, 83056, 107252, 133796, 171565
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OFFSET
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1,3
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COMMENTS
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Also number of ways to choose a sum-preserving permutation of a set partition of a strict partition of n.
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LINKS
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EXAMPLE
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The a(6)=11 twice-partitions are:
((6)),
((5)(1)), ((51)),
((4)(2)), ((42)),
((3)(2)(1)), ((3)(21)), ((21)(3)), ((31)(2)), ((32)(1)), ((321)).
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MATHEMATICA
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nn=20;
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Total[Sum[Times@@Factorial/@Length/@Split[Sort[Total/@ptn]], {ptn, sps[Sort[#]]}]&/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, nn}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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