A114853 a(n) = floor(n^n/n!!).

1, 2, 9, 32, 208, 972, 7843, 43690, 409968, 2604166, 27447010, 193491763, 2241278030, 17224712961, 216027868615, 1787142709274, 24006211998207, 211773735868781, 3021737893128258, 28218694885361552, 424936725846414486

Offset: 1

Author

Jonathan Vos Post, Feb 20 2006

Keywords

• easy
• nonn

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.

Examples

			a(10) = floor((10^10)/3840) = floor(2604166.67) = 2604166.
		

Crossrefs

Cf. A000312, A006882, A055775.

Programs

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 *)

Formula

a(n) = floor(n^n/n!!). a(n) = floor(A000312(n)/A006882(n)).