|
| |
|
|
A103816
|
|
Numerator of Sum_{k=1..n} (-1)^(k+1)/k!.
|
|
5
|
|
|
|
0, 1, 1, 2, 5, 19, 91, 177, 3641, 28673, 28319, 2523223, 27526069, 109339663, 4239014627, 59043418019, 26718637649, 14052333488521, 238063061452591, 158218865944829, 7358312808534631, 124213980448686521, 11277840764547411113, 67527236643922308689
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
COMMENTS
|
Numerator of (n! - A000166(n))/n!.
Numerator of 1 - A053557/A053556.
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 0..250
Eric Weisstein's World of Mathematics, Continued Fraction Constants
Eric Weisstein's World of Mathematics, Generalized Continued Fraction
|
|
|
FORMULA
|
The Aitken delta-squared process leaves the sequence S(n) = Sum_{k=1..n} (-1)^(k+1)/k! essentially unchanged: S(n+3) = (S(n)*S(n+2) - (S(n+1))^2)/(S(n) + S(n+2) - 2*S(n+1)).
|
|
|
MAPLE
|
b:= proc(n) b(n):=`if`(n<2, 1-n, (n-1)*(b(n-1)+b(n-2))) end:
a:= n-> numer((n!-b(n))/n!):
seq(a(n), n=0..30); # Alois P. Heinz, May 15 2013
|
|
|
MATHEMATICA
|
Table[Numerator[Sum[ -(-1)^k/k!, {k, n}]], {n, 0, 22}] (* Robert G. Wilson v *)
Table[Numerator[1 - Subfactorial[n]/n!], {n, 0, 23}] (* Jean-François Alcover, Feb 11 2014 *)
|
|
|
CROSSREFS
|
Cf. A053556 (denominators).
Sequence in context: A205804 A052324 A020115 * A052169 A020019 A020109
Adjacent sequences: A103813 A103814 A103815 * A103817 A103818 A103819
|
|
|
KEYWORD
|
nonn,frac,nice,easy
|
|
|
AUTHOR
|
N. J. A. Sloane, Apr 02 2005
|
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v, Oct 13 2005
|
|
|
STATUS
|
approved
|
| |
|
|
