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.

A114869 s(n) = floor(n^(n/5)/n!!!!!).

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%I A114869 #9 Jun 15 2016 09:19:37
%S A114869 1,0,0,0,1,1,1,1,1,2,2,2,2,3,4,6,5,5,7,10,16,12,14,18,26,39,31,35,45,
%T A114869 64,98,79,88,114,163,249,200,223,291,416,636,511,572,745,1067,1634,
%U A114869 1316,1474,1922,2755,4222,3405,3817,4982,7147,10961,8848,9925,12966
%N A114869 s(n) = floor(n^(n/5)/n!!!!!).
%C A114869 This sequence is an approximation of a quintuple factorial analog to Stirling's approximation to factorial. Note that a(n) is exact for n = 1, 5, 10.
%F A114869 a(n) = floor(n^(n/5)/n!!!). a(n) = floor((A000312(n)^(1/5))/A085157(n)).
%e A114869 a(10) = floor(10^2/10!!!!!) = floor(10^2/50) = floor(2) = 2.
%e A114869 a(15) = floor(15^3/15!!!!!) = floor((15^3)/750) = floor(4.5) = 4.
%e A114869 a(20) = floor(20^4/20!!!!!) = floor((20^4)/15000) = floor(10.6666667) = 10.
%e A114869 a(25) = floor(25^5/25!!!!!) = floor((25^5)/375000) = floor(26.0416667) = 26.
%e A114869 a(30) = floor(30^6/30!!!!!) = floor((30^6)/11250000) = floor(64.8) = 64.
%e A114869 a(35) = floor(35^7/35!!!!!) = floor((35^7)/393750000) = floor(163.401389) = 163.
%t A114869 fac[n_Integer, m_Integer] := Block[{t = n, f = Max[1, n]}, While[t > m, t -= m; f *= t]; f]; a[n_] := Floor[n^(n/5)/fac[n, 5]]; Array[a, 65] (* _Giovanni Resta_, Jun 15 2016 *)
%Y A114869 Cf. A000312, A006882, A055775, A085157.
%K A114869 easy,nonn
%O A114869 1,10
%A A114869 _Jonathan Vos Post_, Feb 20 2006
%E A114869 Corrected and extended by _Giovanni Resta_, Jun 15 2016