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%I #8 Nov 11 2020 09:03:54
%S 1,-1,-3,-3,-1,10,20,36,28,-11,-103,-245,-397,-448,-214,464,1817,3680,
%T 5660,6473,4362,-3232,-18428,-41946,-70589,-94890,-96996,-49673,78907,
%U 317995,673299,1105044,1491333,1605102,1094914,-479358,-3561322,-8404118,-14781724,-21595744,-26450603,-25329527
%N Expansion of Product_{k>=1} (1 - x^k)^(k*(k+1)/2).
%C Convolution inverse of A000294 (Euler transform of the triangular numbers).
%F G.f.: Product_{k>=1} (1 - x^k)^(k*(k+1)/2).
%t nmax = 41; CoefficientList[Series[Product[(1 - x^k)^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]
%o (SageMath) # uses[EulerTransform from A166861]
%o b = EulerTransform(lambda n: -binomial(n+1, 2))
%o print([b(n) for n in range(37)]) # _Peter Luschny_, Nov 11 2020
%Y Cf. A000294, A027999, A028377.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Sep 15 2017