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A304967
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Expansion of Product_{k>=1} 1/(1 - x^k)^(p(k)-p(k-1)), where p(k) = number of partitions of k (A000041).
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6
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1, 0, 1, 1, 3, 3, 8, 9, 20, 26, 49, 68, 123, 173, 295, 432, 707, 1044, 1672, 2483, 3900, 5817, 8993, 13424, 20539, 30609, 46399, 69052, 103879, 154198, 230550, 341261, 507484, 749028, 1108559, 1631340, 2404311, 3527615, 5179317, 7577263, 11086413, 16173577, 23588227
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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G.f.: Product_{k>=1} 1/(1 - x^k)^A002865(k).
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1, add(
(numtheory[sigma](j)-1)*b(n-j), j=1..n)/n)
end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
b(d), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
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MATHEMATICA
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nmax = 42; CoefficientList[Series[Product[1/(1 - x^k)^(PartitionsP[k] - PartitionsP[k - 1]), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (PartitionsP[d] - PartitionsP[d - 1]), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 42}]
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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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