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A307462
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Expansion of Product_{k>=1} (1+x^k)^((-1)^k*k^2).
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5
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1, -1, 5, -14, 36, -97, 246, -593, 1423, -3351, 7699, -17432, 38901, -85545, 185862, -399220, 848080, -1783682, 3716584, -7675916, 15722127, -31951330, 64452707, -129102947, 256876062, -507854808, 997954125, -1949631802, 3787674152, -7319306458, 14071371173
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OFFSET
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0,3
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COMMENTS
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This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = (-1)^(n+1) * n^2, g(n) = -1.
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LINKS
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FORMULA
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a(n) ~ (-1)^n * exp(2*Pi*n^(3/4)/3 + 3*Zeta(3)/(4*Pi^2)) / (4*n^(5/8)). - Vaclav Kotesovec, Apr 09 2019
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Product[(1 + x^k)^((-1)^k*k^2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 09 2019 *)
nmax = 40; CoefficientList[Series[Product[(1 + x^(2*k))^(4*k^2) / (1 + x^(2*k - 1))^((2*k - 1)^2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 09 2019 *)
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PROG
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(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1+x^k)^((-1)^k*k^2)))
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CROSSREFS
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Product_{k>=1} (1+x^k)^((-1)^k*k^b): A083365 (b=0), A284474 (b=1), this sequence (b=2).
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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