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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-Fran├žois 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

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Last modified March 3 09:18 EST 2021. Contains 341760 sequences. (Running on oeis4.)