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A339164
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Number of compositions (ordered partitions) of n into distinct parts, the least being 3.
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8
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0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 50, 50, 80, 104, 134, 158, 212, 356, 410, 578, 752, 1040, 1238, 1646, 1964, 3236, 3674, 5066, 6368, 8720, 10862, 14078, 17180, 22076, 31802, 38378, 49784, 63824, 82670, 104150, 136220, 165980
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OFFSET
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0,8
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} k! * x^(k*(k + 5)/2) / Product_{j=1..k-1} (1 - x^j).
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EXAMPLE
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a(12) = 8 because we have [9, 3], [5, 4, 3], [5, 3, 4], [4, 5, 3], [4, 3, 5], [3, 9], [3, 5, 4] and [3, 4, 5].
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MAPLE
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b:= proc(n, i, p) option remember;
`if`(n=0, p!, `if`((i-3)*(i+4)/2<n, 0,
add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
end:
a:= n-> `if`(n<3, 0, b(n-3$2, 1)):
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MATHEMATICA
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nmax = 49; CoefficientList[Series[Sum[k! x^(k (k + 5)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]
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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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