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Expansion of Product_{k>=1} 1/(1-x^k)^((-1)^k*k^k).
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%I #16 Apr 12 2019 09:00:33

%S 1,-1,4,-31,293,-3499,51284,-891276,17928335,-409921846,10500040633,

%T -297796771914,9262574642871,-313459274848233,11464944476563718,

%U -450647901022275715,18943108018829605740,-847933752191806388254,40266301788890216414608,-2021846883773977115156632

%N Expansion of Product_{k>=1} 1/(1-x^k)^((-1)^k*k^k).

%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = (-1)^n * n^n, g(n) = 1.

%H Seiichi Manyama, <a href="/A307504/b307504.txt">Table of n, a(n) for n = 0..386</a>

%F a(n) ~ (-1)^n * n^n * (1 + exp(-1)/n + (exp(-1)/2 + 4*exp(-2))/n^2). - _Vaclav Kotesovec_, Apr 12 2019

%t nmax=20; CoefficientList[Series[Product[1/(1-x^k)^((-1)^k*k^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 12 2019 *)

%o (PARI) N=20; x='x+O('x^N); Vec(1/prod(k=1, N, (1-x^k)^((-1)^k*k^k)))

%Y Cf. A023880, A266964, A307497.

%K sign

%O 0,3

%A _Seiichi Manyama_, Apr 11 2019