A293568 E.g.f.: exp(x^3/(x^4 - 1)).

1, 0, 0, -6, 0, 0, 360, -5040, 0, -60480, 3628800, -39916800, 19958400, -3113510400, 130767436800, -1318571654400, 3487131648000, -355687428096000, 12813639597158400, -126713646259200000, 1013709170073600000, -85161707377883136000, 2819368492175499264000

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..445

Formula

E.g.f.: Product_{k>0} exp(x^(-(4*k-1))).

D-finite with recurrence: n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n + 5)*(n + 6)*(n + 7)*a(n) + (n + 7)*(n + 6)*(n + 5)*(n + 4)*(n + 3)*(n + 2)*a(n + 1) - 2*(n + 5)*(n + 4)*(n + 7)*(n + 6)*a(n + 4) + 3*(n + 7)*(n + 6)*a(n + 5) + a(n + 8) = 0. - Robert Israel, Feb 22 2026

Maple

f:= gfun:-rectoproc({n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n + 5)*(n + 6)*(n + 7)*a(n) + (n + 7)*(n + 6)*(n + 5)*(n + 4)*(n + 3)*(n + 2)*a(n + 1) - 2*(n + 5)*(n + 4)*(n + 7)*(n + 6)*a(n + 4) + 3*(n + 7)*(n + 6)*a(n + 5) + a(n + 8), a(0)=1, a(1)=0, a(2)=0, a(3)=-6, a(4)=0, a(5)=0, a(6)=360, a(7)=-5040}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Feb 22 2026

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[x^3/(x^4-1)], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Dec 31 2020 *)

Prog

(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x^3/(x^4-1))))
(PARI) N=66; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, exp(x^(4*k-1)))))

Crossrefs

E.g.f.: Product_{k>0} exp(x^(-(m*k-1))): A293532 (m=2), A293567 (m=3), this sequence (m=4).

Cf. A293526.

Sequence in context: A101109 A353224 A293526 * A192072 A397281 A397283

Adjacent sequences: A293565 A293566 A293567 * A293569 A293570 A293571

Keyword

sign

Author

Seiichi Manyama, Oct 12 2017

Status

approved