A293590 E.g.f.: exp(x^3/(1 + x + x^2 + x^3)).
1, 0, 0, 6, -24, 0, 360, 0, -20160, 60480, 1814400, -19958400, -59875200, 2075673600, 21794572800, -860885625600, 3487131648000, 148203095040000, -524638956441600, -71973351075225600, 942749528168448000, 19878836825143296000, -437111394135736320000
Offset: 0
Keywords
Programs
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Mathematica
CoefficientList[Series[E^(x^3/(1 + x + x^2 + x^3)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 13 2017 *) -
PARI
N=66; x='x+O('x^N); Vec(serlaplace(exp(x^3/(1+x+x^2+x^3)))) -
PARI
N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(4*k-1)-x^(4*k)))))
Formula
E.g.f.: Product_{k>0} exp(x^(4*k-1)) / exp(x^(4*k)).