%I #12 Oct 27 2019 18:01:53

%S 1,0,2,-6,12,0,-240,2520,-18480,60480,937440,-21621600,220207680,

%T -311351040,-34490776320,724669545600,-6625031212800,-49471604582400,

%U 3116728731916800,-58942964451571200,335128094882380800,15732203147781120000,-600651799248659558400

%N E.g.f.: exp(x^2/(1 + x + x^2)).

%H Robert Israel, <a href="/A293589/b293589.txt">Table of n, a(n) for n = 0..449</a>

%F E.g.f.: Product_{k>0} exp(x^(3*k-1)) / exp(x^(3*k)).

%F (n+3)*(n+2)*(n+1)*n*a(n)+(2*n+1)*(n+3)*(n+2)*a(n+1)+(3*n+4)*(n+3)*a(n+2)+2*(n+3)*a(n+3)+a(n+4)=0. - _Robert Israel_, Oct 27 2019

%p rec:= (n+3)*(n+2)*(n+1)*n*b(n)+(2*n+1)*(n+3)*(n+2)*b(n+1)+(3*n+4)*(n+3)*b(n+2)+2*(n+3)*b(n+3)+b(n+4)=0:

%p f:= gfun:-rectoproc({rec,b(0)=1,b(1)=0,b(2)=2,b(3)=-6},b(n),remember):

%p map(f, [$0..30]); # _Robert Israel_, Oct 27 2019

%t CoefficientList[Series[E^(x^2/(1 + x + x^2)), {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^2/(1+x+x^2))))

%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(3*k-1)-x^(3*k)))))

%Y Cf. A111884, A293590.

%K sign

%O 0,3

%A _Seiichi Manyama_, Oct 12 2017