cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A114863 #11 Aug 06 2021 16:45:33
%S A114863 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 A114863 733,731,1067,1885,1885,2755,4873,4881,7147,12659,12697,18613,33007,
%U A114863 33143,48638,86337,86777,127463,226454,227795,334864,595382,599342,881657
%N A114863 a(n) = floor(n^(n/3)/n!!!).
%C A114863 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 A114863 Harvey P. Dale, <a href="/A114863/b114863.txt">Table of n, a(n) for n = 1..1000</a>
%F A114863 a(n) = floor(n^(n/3)/n!!!). a(n) = floor((A000312(n)^(1/3))/A007661(n)).
%e A114863 a(9) = floor((9^3)/162) = floor(4.5) = 4.
%e A114863 a(10) = floor((10^3.33333)/280) = floor(7.69381906) = 7.
%e A114863 a(27) = floor((27^9)/7142567040) = floor(1067.62701) = 1067.
%t A114863 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 A114863 Table[Floor[n^(n/3)/Times@@Range[n,1,-3]],{n,50}] (* _Harvey P. Dale_, Aug 06 2021 *)
%Y A114863 Cf. A000312, A006882, A055775, A007661.
%K A114863 easy,nonn
%O A114863 1,6
%A A114863 _Jonathan Vos Post_, Feb 20 2006
%E A114863 More terms from _Giovanni Resta_, Jun 15 2016