A114863 a(n) = floor(n^(n/3)/n!!!).

1, 0, 1, 1, 1, 2, 3, 3, 4, 7, 7, 10, 18, 18, 26, 45, 44, 64, 113, 112, 163, 287, 285, 416, 733, 731, 1067, 1885, 1885, 2755, 4873, 4881, 7147, 12659, 12697, 18613, 33007, 33143, 48638, 86337, 86777, 127463, 226454, 227795, 334864, 595382, 599342, 881657

Offset: 1

Author

Jonathan Vos Post, Feb 20 2006

Keywords

• easy
• nonn

Comments

This sequence is an approximation of a triple factorial analog to Stirling's approximation to factorial. Note that a(n) is exact for n = 1, 3, 6.

Examples

			a(9) = floor((9^3)/162) = floor(4.5) = 4.
a(10) = floor((10^3.33333)/280) = floor(7.69381906) = 7.
a(27) = floor((27^9)/7142567040) = floor(1067.62701) = 1067.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000312, A006882, A055775, A007661.

Programs

Mathematica

fac[n_, m_] := Block[{t = n, f = Max[1, n]}, While[t > m, t -= m; f *= t]; f]; a[n_] := Floor[n^(n/3)/fac[n, 3]]; Array[a, 40] (* Giovanni Resta, Jun 15 2016 *)
Table[Floor[n^(n/3)/Times@@Range[n,1,-3]],{n,50}] (* Harvey P. Dale, Aug 06 2021 *)

Formula

a(n) = floor(n^(n/3)/n!!!). a(n) = floor((A000312(n)^(1/3))/A007661(n)).

Extensions

More terms from Giovanni Resta, Jun 15 2016