%I #6 Jul 11 2015 10:43:26

%S 1,0,0,1,1,1,1,2,3,2,3,4,7,6,7,10,17,14,18,26,41,36,44,64,104,91,112,

%T 163

%N a(n) = floor(n^(n/4)/n!!!!).

%C This sequence is an approximation to a quadruple factorial analog of Stirling's approximation to the factorial function. Note that a(n) is exact for n = 1, 4, 8.

%F a(n) = floor(n^(n/4)/n!!!). a(n) = floor((A000312(n)^(1/4))/A007662(n)).

%e a(8) = floor((8^2)/8!!!!) = floor((8^2)/32) = floor(2) = 2.

%e a(9) = floor((9^2.25)/9!!!!) = floor((9^2.25)/45) = floor(3.11769145) = 3.

%e a(16) = floor((16^4)/16!!!!) = floor((16^4)/6144) = floor(10.6666667) = 10.

%e a(20) = floor((20^5)/20!!!!) = floor((20^5)/122880) = floor(26.0416667) = 26.

%Y Cf. A000312, A006882, A055775, A007662.

%K easy,nonn

%O 1,8

%A _Jonathan Vos Post_, Feb 20 2006