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A341241
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Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^3.
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9
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1, 0, 3, 3, 6, 9, 13, 21, 27, 40, 54, 75, 97, 129, 171, 220, 282, 360, 460, 576, 720, 896, 1116, 1374, 1682, 2061, 2517, 3050, 3684, 4449, 5354, 6414, 7656, 9135, 10875, 12891, 15243, 18015, 21243, 24966, 29286, 34326, 40156, 46851, 54573, 63509, 73794, 85551, 99035, 114555
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OFFSET
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3,3
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LINKS
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Table of n, a(n) for n=3..52.
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FORMULA
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G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^3.
a(n) ~ A107635(n). - Vaclav Kotesovec, Feb 20 2021
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MAPLE
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g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
[1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
end:
b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),
(q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
end:
a:= n-> b(n, 3):
seq(a(n), n=3..52); # Alois P. Heinz, Feb 07 2021
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MATHEMATICA
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nmax = 52; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^3, {x, 0, nmax}], x] // Drop[#, 3] &
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CROSSREFS
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Cf. A000700, A022598, A047655, A107635, A327381, A338463, A341221, A341243, A341244, A341245, A341246, A341247, A341251.
Sequence in context: A280240 A058628 A035528 * A300300 A293675 A050337
Adjacent sequences: A341238 A341239 A341240 * A341242 A341243 A341244
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Feb 07 2021
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STATUS
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approved
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