login
A114853
a(n) = floor(n^n/n!!).
1
1, 2, 9, 32, 208, 972, 7843, 43690, 409968, 2604166, 27447010, 193491763, 2241278030, 17224712961, 216027868615, 1787142709274, 24006211998207, 211773735868781, 3021737893128258, 28218694885361552, 424936725846414486
OFFSET
1,2
COMMENTS
This is to double factorial A006882 as A055775 "Floor(n^n/n!)" is to factorial. This sequence is a weak first approximation of a double factorial analog to Stirling's approximation to factorial. Note that a(n) is exact for n = 1, 2, 3, 4, 6.
FORMULA
a(n) = floor(n^n/n!!). a(n) = floor(A000312(n)/A006882(n)).
EXAMPLE
a(10) = floor((10^10)/3840) = floor(2604166.67) = 2604166.
MAPLE
A114853 := proc(n)
n^n/doublefactorial(n) ;
floor(%) ;
end proc:
seq(A114853(n), n=1..25) ; # R. J. Mathar, Jun 23 2014
MATHEMATICA
Table[Floor[n^n/n!!], {n, 30}] (* Harvey P. Dale, Jul 29 2023 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 20 2006
STATUS
approved