A120265 a(n) = numerator(Sum_{k=1..n} 1/k!).

1, 3, 5, 41, 103, 1237, 433, 69281, 62353, 6235301, 8573539, 164611949, 5349888343, 29959374721, 561738276019, 35951249665217, 4701317263913, 11001082397556421, 52255141388393, 4180411311071440001, 43894318766250120011, 386270005143001056097

Offset: 1

Author

Alexander Adamchuk, Jun 30 2006

Keywords

• frac
• nonn

Examples

			1, 3/2, 5/3, 41/24, 103/60, 1237/720, 433/252, 69281/40320, 62353/36288, 6235301/3628800, 8573539/4989600, 164611949/
95800320, 5349888343/3113510400, ...
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A061354, A061355 (denominator).

Programs

Maple

a:= n-> numer(add(1/i!, i=1..n)): seq(a(n), n=1..23); # Zerinvary Lajos, Mar 28 2007

Mathematica

Numerator[Table[Sum[1/k!,{k,1,n}],{n,1,30}]]

PARI

a(n) = numerator(sum(k=1, n, 1/k!)); \\ Michel Marcus, Jun 01 2018

Formula

A061355(n) = denominator(Sum_{k=1..n} 1/k!).

a(n) = A061354(n) - A061355(n).

a(n) = numerator(exp(1)*gamma(n + 1,1)/gamma(n + 1) - 1). - Gerry Martens, May 31 2018

(exp(x)-1) / (1-x) is the o.g.f. for the sequence of fractions. - Joerg Arndt, Jun 01 2018