A114868 a(n) = floor(n^(n/4)/n!!!!).

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, 163

Offset: 1

Author

Jonathan Vos Post, Feb 20 2006

Keywords

• easy
• nonn

Comments

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.

Examples

			a(8) = floor((8^2)/8!!!!) = floor((8^2)/32) = floor(2) = 2.
a(9) = floor((9^2.25)/9!!!!) = floor((9^2.25)/45) = floor(3.11769145) = 3.
a(16) = floor((16^4)/16!!!!) = floor((16^4)/6144) = floor(10.6666667) = 10.
a(20) = floor((20^5)/20!!!!) = floor((20^5)/122880) = floor(26.0416667) = 26.
		

Crossrefs

Cf. A000312, A006882, A055775, A007662.

Formula

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