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

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..449

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

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 *)

Prog

(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)))))

Crossrefs

Cf. A111884, A293590.

Sequence in context: A342544 A342540 A328449 * A293117 A293122 A014452

Adjacent sequences: A293586 A293587 A293588 * A293590 A293591 A293592

Keyword

sign

Author

Seiichi Manyama, Oct 12 2017

Status

approved