A293567 Expansion of e.g.f.: exp(x^2/(x^3 - 1)).

1, 0, -2, 0, 12, -120, -120, 5040, -38640, -181440, 5412960, -33264000, -478336320, 12194582400, -50871300480, -2168559993600, 49692144902400, -59775248332800, -15819216007795200, 329479616206540800, 1101564635255884800, -174845824790757120000

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

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

D-finite with recurrence: n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n + 5)*a(n) + (n + 5)*(n + 4)*(n + 3)*(n + 2)*a(n + 1) - 2*(n + 5)*(n + 4)*(n + 3)*a(n + 3) + 2*a(n + 4)*(n + 5) + a(n + 6) = 0. - Robert Israel, Feb 22 2026

Maple

f:= gfun:-rectoproc({n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n + 5)*a(n) + (n + 5)*(n + 4)*(n + 3)*(n + 2)*a(n + 1) - 2*(n + 5)*(n + 4)*(n + 3)*a(n + 3) + 2*a(n + 4)*(n + 5) + a(n + 6), a(0)=1, a(1)=0, a(2)=-2, a(3)=0, a(4)=12, a(5)=-120}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Feb 22 2026

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[x^2/(x^3-1)], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 31 2024 *)

Prog

(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x^2/(x^3-1))))
(PARI) N=66; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, exp(x^(3*k-1)))))

Crossrefs

E.g.f.: Product_{k>0} exp(x^(-(m*k-1))): A293532 (m=2), this sequence (m=3), A293568 (m=4).

Cf. A293494.

Sequence in context: A383994 A013310 A269889 * A293494 A058803 A193202

Adjacent sequences: A293564 A293565 A293566 * A293568 A293569 A293570

Keyword

sign

Author

Seiichi Manyama, Oct 12 2017

Extensions

Definition clarified by Harvey P. Dale, Mar 31 2024

Status

approved