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A270917
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Coefficient of x^n in Product_{k>=1} (1 + x^k)^(k^n).
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9
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1, 1, 4, 35, 457, 12421, 678101, 69540142, 13730026114, 5551573311817, 4379029522335786, 6705866900012021577, 21038900445652125741759, 131183458646068931932668114, 1603688863449847489871671547959, 40294004792352613617780682256221711
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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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Conjecture: limit n->infinity a(n)^(1/n^2) = exp(exp(-1)) = 1.444667861...
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MAPLE
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b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1, k)*binomial(i^k, j), j=0..n/i)))
end:
a:= n-> b(n$3):
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MATHEMATICA
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Table[SeriesCoefficient[Product[(1+x^k)^(k^n), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
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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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