A246607 Expansion of e.g.f. exp(x - x^3).

1, 1, 1, -5, -23, -59, 241, 2311, 9745, -30743, -529919, -3161069, 6984121, 216832045, 1696212337, -2117117729, -138721306079, -1359994188719, 367573878145, 127713732858667, 1523067770484361, 1104033549399061, -159815269852521359, -2270787199743845705, -3946710127731620303

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

From Seiichi Manyama, Feb 25 2022: (Start)

a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-2*k,k)/(n-2*k)!.

a(n) = a(n-1) - 3! * binomial(n-1,2) * a(n-3) for n > 2. (End)

Mathematica

Range[0, 24]! CoefficientList[Series[Exp[x - x^3], {x, 0, 24}], x] (* Robert G. Wilson v, Aug 31 2014, with correction from Vincenzo Librandi *)

Prog

(PARI) default(seriesprecision, 30); serlaplace(exp(x-x^3)) \\ Michel Marcus, Aug 31 2014
(PARI) a(n) = n!*sum(k=0, n\3, (-1)^k*binomial(n-2*k, k)/(n-2*k)!); \\ Seiichi Manyama, Feb 25 2022
(PARI) a(n) = if(n<3, 1, a(n-1)-3!*binomial(n-1, 2)*a(n-3)); \\ Seiichi Manyama, Feb 25 2022

Crossrefs

Cf. A118395, A293604.

Sequence in context: A075565 A075707 A126420 * A116581 A337750 A093622

Adjacent sequences: A246604 A246605 A246606 * A246608 A246609 A246610

Keyword

sign

Author

Robert G. Wilson v, Aug 31 2014

Status

approved