A293589 E.g.f.: exp(x^2/(1 + x + x^2)).
1, 0, 2, -6, 12, 0, -240, 2520, -18480, 60480, 937440, -21621600, 220207680, -311351040, -34490776320, 724669545600, -6625031212800, -49471604582400, 3116728731916800, -58942964451571200, 335128094882380800, 15732203147781120000, -600651799248659558400
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..449
Programs
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Maple
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: f:= gfun:-rectoproc({rec,b(0)=1,b(1)=0,b(2)=2,b(3)=-6},b(n),remember): map(f, [$0..30]); # Robert Israel, Oct 27 2019 -
Mathematica
CoefficientList[Series[E^(x^2/(1 + x + x^2)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 13 2017 *) -
PARI
N=66; x='x+O('x^N); Vec(serlaplace(exp(x^2/(1+x+x^2)))) -
PARI
N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(3*k-1)-x^(3*k)))))
Formula
E.g.f.: Product_{k>0} exp(x^(3*k-1)) / exp(x^(3*k)).
(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