A114854 a(n) = floor(n^(n/2)/n!!).

1, 1, 1, 2, 3, 4, 8, 10, 20, 26, 51, 64, 128, 163, 326, 416, 834, 1067, 2148, 2755, 5559, 7147, 14449, 18613, 37696, 48638, 98650, 127463, 258857, 334864, 680822, 881657, 1794294, 2325750, 4737361

Offset

1,4

Comments

This sequence is a second approximation of a double factorial analog to Stirling's approximation to factorial. Note that a(n) is exact for n = 1, 2, 4.

Links

Table of n, a(n) for n=1..35.

Formula

a(n) = floor(n^(n/2)/n!!). a(n) = floor(sqrt(A000312(n))/A006882(n)).

Example

a(10) = floor((10^5)/3840) = floor(26.0416667) = 26.
a(11) = floor((11^5.5)/10395) = floor(51.3848715) = 51.

Maple

A114854 := proc(n)
    n^(n/2)/doublefactorial(n) ;
    floor(%) ;
end proc:
seq(A114854(n), n=1..35) ; # R. J. Mathar, Jun 23 2014

Mathematica

Table[Floor[n^(n/2)/n!!], {n, 40}] (* Harvey P. Dale, Apr 04 2019 *)

Crossrefs

Cf. A000312, A006882, A055775.

Sequence in context: A295296 A186417 A207644 * A127279 A106131 A275646

Adjacent sequences: A114851 A114852 A114853 * A114855 A114856 A114857

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 20 2006

Status

approved