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A237999
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Number of partitions of 2^n into parts that are at most n with at least one part of each size.
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6
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0, 1, 1, 2, 9, 119, 4935, 596763, 211517867, 224663223092, 734961197081208, 7614278809664610952, 256261752606028225485183, 28642174350851846128820426827, 10830277060032417592098008847162727, 14068379226083299071248895931891435683229
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OFFSET
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0,4
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COMMENTS
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Also the number of strict integer partitions of 2^n with n parts. For example, the a(1) = 1 through a(4) = 9 partitions are (A = 10):
(2) (31) (431) (6532)
(521) (6541)
(7432)
(7531)
(7621)
(8431)
(8521)
(9421)
(A321)
(End)
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LINKS
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FORMULA
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a(n) = [x^(2^n-n*(n+1)/2)] Product_{j=1..n} 1/(1-x^j).
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EXAMPLE
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a(1) = 1: 11.
a(2) = 1: 211.
a(3) = 2: 3221, 32111.
a(4) = 9: 433321, 443221, 4322221, 4332211, 4432111, 43222111, 43321111, 432211111, 4321111111.
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MATHEMATICA
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a[n_] := SeriesCoefficient[Product[1/(1 - x^j), {j, 1, n}], {x, 0, 2^n - n*(n + 1)/2}];
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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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