A130906 Expansion of e.g.f. exp(x^3/3!)/(1-x).

1, 1, 2, 7, 28, 140, 850, 5950, 47600, 428680, 4286800, 47154800, 565873000, 7356349000, 102988886000, 1544834691400, 24717355062400, 420195036060800, 7563510839684800, 143706705954011200, 2874134119080224000, 60356816536896880000, 1327849963811731360000

Offset: 0

Author

Karol A. Penson, Jun 08 2007

Keywords

• nonn

Crossrefs

Cf. A000522, A130905.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[x^3/6]/(1-x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 10 2018 *)

Formula

a(n) ~ n! * exp(1/6). - Vaclav Kotesovec, Aug 04 2014

a(n) = n! * Sum_{k=0..floor(n/3)} 1/(6^k * k!). - Seiichi Manyama, Feb 27 2024

Extensions

More terms from Harvey P. Dale, May 10 2018