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A114863 a(n) = floor(n^(n/3)/n!!!). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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.

LINKS

Table of n, a(n) for n=1..48.

FORMULA

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A000312, A006882, A055775, A007661.

Sequence in context: A119614 A260167 A035540 * A152980 A170891 A035535

Adjacent sequences:  A114860 A114861 A114862 * A114864 A114865 A114866

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 20 2006

EXTENSIONS

More terms from Giovanni Resta, Jun 15 2016

STATUS

approved

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Last modified November 19 08:44 EST 2019. Contains 329318 sequences. (Running on oeis4.)