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%I #17 Apr 12 2019 10:22:42
%S 1,1,-3,24,-226,2791,-42467,761826,-15714798,366401751,-9528266885,
%T 273439284005,-8584541521286,292695692569785,-10771202678289501,
%U 425538242701632216,-17964593967281888258,807094224863059707077,-38449142619220645357810,1935991142823285710574298
%N Expansion of Product_{k>=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+1) * n^n, g(n) = 1.
%H Seiichi Manyama, <a href="/A307514/b307514.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 + 3*exp(-2))/n^2). - _Vaclav Kotesovec_, Apr 12 2019
%t nmax=20; CoefficientList[Series[Product[(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(prod(k=1, N, (1-x^k)^((-1)^k*k^k)))
%Y Cf. A010054, A266964, A281781, A283499, A307460, A307497, A307504.
%K sign
%O 0,3
%A _Seiichi Manyama_, Apr 12 2019