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A307497
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Expansion of Product_{k>=1} (1+x^k)^((-1)^k*k^k).
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3
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1, -1, 5, -32, 294, -3527, 51589, -894706, 17978610, -410803143, 10517824035, -298204099693, 9273022031794, -313755862498513, 11474175971184267, -450960476552715192, 18954545423649435646, -848383466771831169101, 40285210722052785437974
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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^n, g(n) = -1.
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LINKS
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FORMULA
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a(n) ~ (-1)^n * n^n * (1 + exp(-1)/n + (exp(-1)/2 + 5*exp(-2))/n^2). - Vaclav Kotesovec, Apr 12 2019
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MATHEMATICA
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nmax=20; CoefficientList[Series[Product[(1+x^k)^((-1)^k*k^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 12 2019 *)
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PROG
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(PARI) N=20; x='x+O('x^N); Vec(prod(k=1, N, (1+x^k)^((-1)^k*k^k)))
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CROSSREFS
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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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