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A317912
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Expansion of Product_{k>=2} 1/(1 - k*x^k).
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2
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1, 0, 2, 3, 8, 11, 31, 41, 101, 156, 318, 498, 1037, 1555, 3024, 4889, 8849, 14112, 25622, 40322, 71314, 113926, 194677, 310819, 530030, 835484, 1400523, 2226307, 3668998, 5797558, 9521310, 14942262, 24298136, 38187102, 61384028, 96161997, 154078991, 239891926, 381723396
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OFFSET
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0,3
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COMMENTS
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Sum of products of terms in all partitions of n into parts >= 2.
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LINKS
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FORMULA
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G.f.: exp(Sum_{j>=1} Sum_{k>=2} k^j*x^(j*k)/j).
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EXAMPLE
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a(6) = 31 because we have [6], [4, 2], [3, 3], [2, 2, 2] and 6 + 4*2 + 3*3 + 2*2*2 = 31.
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
b(n, i-1)+ i*b(n-i, min(n-i, i)))
end:
a:= n-> b(n$2) -`if`(n=0, 0, b(n-1$2)):
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MATHEMATICA
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nmax = 38; CoefficientList[Series[Product[1/(1 - k x^k), {k, 2, nmax}], {x, 0, nmax}], x]
nmax = 38; CoefficientList[Series[Exp[Sum[Sum[k^j x^(j k)/j, {k, 2, nmax}], {j, 1, nmax}]], {x, 0, nmax}], x]
b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d^(k/d + 1), {d, Divisors[k]}] b[n - k], {k, 1, n}]/n]; Differences[Table[b[n], {n, -1, 38}]]
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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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