|
|
A052169
|
|
Equivalent of the Kurepa hypothesis for left factorial.
|
|
5
|
|
|
1, 2, 5, 19, 91, 531, 3641, 28673, 254871, 2523223, 27526069, 328018989, 4239014627, 59043418019, 881715042417, 14052333488521, 238063061452591, 4271909380510383, 80941440893880941, 1614781745832924773, 33833522293642233339, 742799603083145395579
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,2
|
|
LINKS
|
|
|
FORMULA
|
a(2) = 1, a(3) = 2, a(n) = (n-2)*a(n-1) + (n-3)*a(n-2).
a(n) = 2*floor((n+1)!*(n+3)/e+1/2) - 3*(floor(((n+1)!+1)/e)+ floor(((n+2)!+1)/e)) +(n+1)!+(n+2)!, n>1, with offset 0..a(0)= 1. - Gary Detlefs, Apr 18 2010
a(n) = 1/(n+1)*((n+2)!-floor(((n+2)!+1)/e)), with offset 0 a(n) = 1/(n-1)*(n! - floor((n!+1)/e)). - Gary Detlefs, Jul 11 2010
Let y(-1)=1, y(0)=1, and y(n) = (Sum_{k=0..n-1} y(k)+y(k-1))/n,
a(n) = (n-2)!*y(n-2).
(End)
a(n) = (Gamma(n+1,0)-exp(-1)*Gamma(n+1,-1))/(n-1). - Martin Clever, Mar 25 2023
|
|
MAPLE
|
a[2] := 1: a[3] := 2: for n from 4 to 21 do a[n] := (n-2)*a[n-1]+(n-3)*a[n-2] end do: seq(a[n], n = 2 .. 21); # Emeric Deutsch, Jun 15 2009
# second Maple program:
a:= proc(n) option remember; `if`(n<4, n-1,
(n-2)*a(n-1)+(n-3)*a(n-2))
end:
|
|
MATHEMATICA
|
Numerator[k=1; NestList[1+1/(k++ #1)&, 1, 12]] (* Wouter Meeussen, Mar 24 2007 *)
|
|
PROG
|
(Sage) from sage.combinat.sloane_functions import ExtremesOfPermanentsSequence2 ; e = ExtremesOfPermanentsSequence2() ; it = e.gen(1, 2, 1) ; [next(it) for i in range(20)] #(5 rows) # Zerinvary Lajos, May 15 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|