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A301756
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Number of ways to choose disjoint strict rooted partitions of each part in a strict rooted partition of n.
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1
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1, 1, 1, 2, 3, 5, 7, 10, 15, 22, 30, 42, 60, 85, 114, 155, 206, 286, 394, 524, 683, 910, 1187, 1564, 2090, 2751, 3543, 4606, 5917, 7598, 9771, 12651, 16260, 20822, 26421, 33525, 42463, 53594, 67337, 85299
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OFFSET
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1,4
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COMMENTS
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A rooted partition of n is an integer partition of n - 1.
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LINKS
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EXAMPLE
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The a(8) = 10 rooted twice-partitions:
(6), (51), (42), (321),
(5)(), (41)(), (32)(), (4)(1), (3)(2),
(3)(1)().
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MATHEMATICA
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twirtns[n_]:=Join@@Table[Tuples[IntegerPartitions[#-1]&/@ptn], {ptn, IntegerPartitions[n-1]}];
Table[Select[twirtns[n], And[UnsameQ@@Total/@#, UnsameQ@@Join@@#]&]//Length, {n, 20}]
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CROSSREFS
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Cf. A002865, A032305, A063834, A093637, A275780, A279375, A294786, A301422, A301462, A301467, A301480, A301706.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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