Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Aug 06 2021 16:45:33
%S 1,0,1,1,1,2,3,3,4,7,7,10,18,18,26,45,44,64,113,112,163,287,285,416,
%T 733,731,1067,1885,1885,2755,4873,4881,7147,12659,12697,18613,33007,
%U 33143,48638,86337,86777,127463,226454,227795,334864,595382,599342,881657
%N a(n) = floor(n^(n/3)/n!!!).
%C 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.
%H Harvey P. Dale, <a href="/A114863/b114863.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = floor(n^(n/3)/n!!!). a(n) = floor((A000312(n)^(1/3))/A007661(n)).
%e a(9) = floor((9^3)/162) = floor(4.5) = 4.
%e a(10) = floor((10^3.33333)/280) = floor(7.69381906) = 7.
%e a(27) = floor((27^9)/7142567040) = floor(1067.62701) = 1067.
%t 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 *)
%t Table[Floor[n^(n/3)/Times@@Range[n,1,-3]],{n,50}] (* _Harvey P. Dale_, Aug 06 2021 *)
%Y Cf. A000312, A006882, A055775, A007661.
%K easy,nonn
%O 1,6
%A _Jonathan Vos Post_, Feb 20 2006
%E More terms from _Giovanni Resta_, Jun 15 2016