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A320696
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Number of partitions of n with up to nine distinct kinds of 1.
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2
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1, 9, 37, 94, 173, 266, 388, 568, 826, 1176, 1641, 2256, 3064, 4115, 5472, 7215, 9437, 12250, 15798, 20253, 25813, 32721, 41277, 51836, 64813, 80700, 100093, 123707, 152370, 187047, 228895, 279284, 339806, 412322, 499014, 602430, 725543, 871815, 1045274
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ Pi * 2^(13/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018
G.f.: (1 + x)^9 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0 or i=1,
binomial(9, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
end:
a:= n-> b(n$2):
seq(a(n), n=0..60);
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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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