A351929 Expansion of e.g.f. exp(x - x^3/6).

1, 1, 1, 0, -3, -9, -9, 36, 225, 477, -819, -10944, -37179, 16875, 870507, 4253796, 2481921, -101978919, -680495175, -1060229088, 16378166061, 145672249311, 368320357791, -3415036002300, -40270115077983, -141926533828299, 882584266861701, 13970371667206176

Offset

0,5

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (-1/6)^k * binomial(n-2*k,k)/(n-2*k)!.

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

Mathematica

m = 27; Range[0, m]! * CoefficientList[Series[Exp[x - x^3/6], {x, 0, m}], x] (* Amiram Eldar, Feb 26 2022 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x-x^3/6)))
(PARI) a(n) = n!*sum(k=0, n\3, (-1/3!)^k*binomial(n-2*k, k)/(n-2*k)!);
(PARI) a(n) = if(n<3, 1, a(n-1)-binomial(n-1, 2)*a(n-3));

Crossrefs

Cf. A351930, A351931.

Cf. A190865, A246607.

Sequence in context: A125824 A203558 A223653 * A238912 A038227 A080292

Adjacent sequences: A351926 A351927 A351928 * A351930 A351931 A351932

Keyword

sign

Author

Seiichi Manyama, Feb 26 2022

Status

approved