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A114968 a(n) = floor(n^(n/6)/n!!!!!!).

%I A114968 #8 Jun 15 2016 09:19:28
%S A114968 1,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,3,4,6,4,4,5,7,10,15,11,12,14,18,26,
%T A114968 37,28,29,35,46,64,94,71,74,89,117,163,238,180,188,226,297,416,608,
%U A114968 461,481,580,763,1067,1563,1187,1240,1496,1969,2755,4038,3070
%N A114968 a(n) = floor(n^(n/6)/n!!!!!!).
%C A114968 This sequence is an approximation of a sextuple factorial analog to Stirling's approximation to factorial. Note that a(n) is exact for n = 1, 6, 8, 9, 12.
%F A114968 a(n) = floor(n^(n/6)/n!!!!!!). a(n) = floor(n^(n/6)/n!6). a(n) = floor((A000312(n)^(1/6))/A085158(n)).
%e A114968 a(12) = floor(12^2/12!!!!!) = floor(12^2/72) = floor(2) = 2.
%e A114968 a(18) = floor(18^3/18!!!!!) = floor((18^3)/1296) = floor(4.5) = 4.
%e A114968 a(24) = floor(24^4/20!!!!!) = floor((24^4)/31104) = floor(10.6666667) = 10.
%e A114968 a(30) = floor(30^5/25!!!!!) = floor((30^5)/933120) = floor(26.0416667) = 26.
%e A114968 a(36) = floor(36^6/30!!!!!) = floor((36^6)/33592320) = floor(64.8) = 64.
%t A114968 fac[n_, m_] := Block[{t = n, f = Max[1, n]}, While[t > m, t -= m; f *= t]; f]; a[n_] := Floor[n^(n/6)/fac[n, 6]]; Array[a, 65] (* _Giovanni Resta_, Jun 15 2016 *)
%Y A114968 Cf. A000312, A006882, A055775, A085157, A085158.
%K A114968 easy,nonn
%O A114968 1,12
%A A114968 _Jonathan Vos Post_, Feb 22 2006
%E A114968 Corrected and extended by _Giovanni Resta_, Jun 15 2016