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A259373
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a(n) = Product_{k=0..n} p(k)^k, where p(k) is the partition function A000041.
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5
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1, 1, 4, 108, 67500, 1134472500, 2009787236572500, 343390991123754492187500, 18843880602308850038793150000000000, 370904101895245095313565571450000000000000000000, 6335115544513765517772271190776403515352524800000000000000000000
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ c * Product_{k=1..n} ( (exp(Pi*sqrt(2/3*(k-1/24))) / (4*sqrt(3)*(k-1/24)) * (1 - sqrt(3/(2*(k-1/24)))/Pi)) )^k, where c = A259405 = 0.90866166764445489256...
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MATHEMATICA
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Table[Product[PartitionsP[k]^k, {k, 0, n}], {n, 0, 10}]
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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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