A370696 Expansion of e.g.f. exp(x^3)/(1-x).

1, 1, 2, 12, 48, 240, 1800, 12600, 100800, 967680, 9676800, 106444800, 1297296000, 16864848000, 236107872000, 3552515366400, 56840245862400, 966284179660800, 17402007419596800, 330638140972339200, 6612762819446784000, 138878156300083200000

Offset

0,3

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} 1/k!.

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[x^3]/(1-x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 13 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3)/(1-x)))
(PARI) a(n) = n!*sum(k=0, n\3, 1/k!);

Crossrefs

Cf. A000522, A355268.

Cf. A130906.

Sequence in context: A347324 A333728 A354131 * A052569 A221663 A232663

Adjacent sequences: A370693 A370694 A370695 * A370697 A370698 A370699

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 27 2024

Status

approved