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A309172
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Expansion of Product_{k>=1} 1/(1 - (1 + x + x^2) * x^k).
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1
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1, 1, 3, 7, 15, 31, 64, 128, 254, 496, 961, 1844, 3516, 6662, 12564, 23593, 44153, 82385, 153351, 284857, 528235, 978148, 1809120, 3342722, 6171318, 11385733, 20994298, 38693809, 71288111, 131297855, 241761727, 445068646, 819205061, 1507641487, 2774307387, 5104712633
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..35.
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FORMULA
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G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (1 + x + x^2)^d/d).
a(n) ~ 1/((1 + 2*r + 3*r^2) * QPochhammer[r] * r^(n+1)), where r = A192918. - Vaclav Kotesovec, Jul 16 2019
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MATHEMATICA
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nmax = 35; CoefficientList[Series[Product[1/(1 - (1 + x + x^2) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 35; CoefficientList[Series[Exp[Sum[x^k Sum[(1 + x + x^2)^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x]
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CROSSREFS
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Cf. A160571, A227681, A309173.
Sequence in context: A351754 A174743 A146686 * A178459 A129984 A351707
Adjacent sequences: A309169 A309170 A309171 * A309173 A309174 A309175
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Jul 15 2019
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STATUS
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approved
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