A293494 E.g.f.: exp(x^2/(1 - x^3)).

1, 0, 2, 0, 12, 120, 120, 5040, 42000, 181440, 5473440, 46569600, 479666880, 12713500800, 123519876480, 2190354566400, 54922842374400, 652587628492800, 16192687807296000, 400439258111692800, 5994400896144460800, 182793304684134144000, 4590673238662192281600

Offset

0,3

Links

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

Formula

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

a(n) ~ exp(2*sqrt(3*n)/3 - n - 1/6) * n^(n-1/4) / (sqrt(2) * 3^(1/4)). - Vaclav Kotesovec, Oct 10 2017

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

Prog

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

Crossrefs

Cf. A293493.

Sequence in context: A013310 A269889 A293567 * A058803 A193202 A294463

Adjacent sequences: A293491 A293492 A293493 * A293495 A293496 A293497

Keyword

nonn

Author

Seiichi Manyama, Oct 10 2017

Status

approved