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A261561
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Expansion of Product_{k>=1} (1/(1 - 2*x^k))^k.
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5
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1, 2, 8, 22, 64, 162, 424, 1022, 2480, 5770, 13336, 30046, 67184, 147554, 321592, 692278, 1479568, 3133474, 6596008, 13788606, 28679264, 59335530, 122256456, 250875550, 513116864, 1046190786, 2127557592, 4316282006, 8739096992, 17661731138, 35639764536
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ c * 2^n, where c = Product_{j>=1} 1/(1 - 1/2^j)^(j+1) = 34.7387234654851595844514193757064296508992247003230539635669599773458896...
G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} 2^d * n^2/d^2 ). - Paul D. Hanna, Sep 30 2015
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(2^j*binomial(i+j-1, j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> b(n$2):
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MATHEMATICA
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nmax = 50; CoefficientList[Series[Product[(1/(1 - 2*x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 50; CoefficientList[Series[Exp[Sum[2^k/k*x^k/(1 - x^k)^2, {k, 1, nmax}]], {x, 0, nmax}], x]
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PROG
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(PARI) {a(n) = polcoeff( exp( sum(m=1, n, x^m/m * sumdiv(m, d, 2^d*m^2/d^2) ) +x*O(x^n)), n)}
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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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