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A320319
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Number of weakly unimodal compositions of n in which the greatest part occurs exactly eight times.
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2
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1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 16, 20, 27, 34, 45, 56, 73, 90, 115, 142, 179, 220, 276, 338, 421, 516, 638, 780, 962, 1172, 1438, 1750, 2138, 2594, 3159, 3822, 4638, 5600, 6771, 8154, 9834, 11812, 14203, 17024
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OFFSET
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0,18
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LINKS
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FORMULA
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G.f.: Sum_{n>=0} x^(8*n) / Product_{j=1..n-1} (1-x^j)^2.
a(n) ~ Pi^7 * 7! * exp(2*Pi*sqrt(n/3)) / (2^10 * 3^(17/4) * n^(19/4)). - Vaclav Kotesovec, Oct 24 2018
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MAPLE
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b:= proc(n, i) option remember; `if`(i>n, 0,
`if`(8*i=n, 1, 0)+add(b(n-i*j, i+1)*(j+1), j=0..n/i))
end:
a:= n-> `if`(n=0, 1, b(n, 1)):
seq(a(n), n=0..70);
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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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