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%I #7 Oct 13 2017 05:28:47
%S 1,0,0,6,-24,0,360,0,-20160,60480,1814400,-19958400,-59875200,
%T 2075673600,21794572800,-860885625600,3487131648000,148203095040000,
%U -524638956441600,-71973351075225600,942749528168448000,19878836825143296000,-437111394135736320000
%N E.g.f.: exp(x^3/(1 + x + x^2 + x^3)).
%F E.g.f.: Product_{k>0} exp(x^(4*k-1)) / exp(x^(4*k)).
%t CoefficientList[Series[E^(x^3/(1 + x + x^2 + x^3)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Oct 13 2017 *)
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x^3/(1+x+x^2+x^3))))
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(4*k-1)-x^(4*k)))))
%Y Cf. A111884, A293589.
%K sign
%O 0,4
%A _Seiichi Manyama_, Oct 12 2017
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