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%I #35 Feb 19 2023 17:01:26
%S 1,3,5,41,103,1237,433,69281,62353,6235301,8573539,164611949,
%T 5349888343,29959374721,561738276019,35951249665217,4701317263913,
%U 11001082397556421,52255141388393,4180411311071440001,43894318766250120011,386270005143001056097
%N a(n) = numerator(Sum_{k=1..n} 1/k!).
%H M. F. Hasler, <a href="/A120265/b120265.txt">Table of n, a(n) for n = 1..100</a>
%F A061355(n) = denominator(Sum_{k=1..n} 1/k!).
%F a(n) = A061354(n) - A061355(n).
%F a(n) = numerator(exp(1)*gamma(n + 1,1)/gamma(n + 1) - 1). - _Gerry Martens_, May 31 2018
%F (exp(x)-1) / (1-x) is the o.g.f. for the sequence of fractions. - _Joerg Arndt_, Jun 01 2018
%e 1, 3/2, 5/3, 41/24, 103/60, 1237/720, 433/252, 69281/40320, 62353/36288, 6235301/3628800, 8573539/4989600, 164611949/
%e 95800320, 5349888343/3113510400, ...
%p a:= n-> numer(add(1/i!, i=1..n)): seq(a(n), n=1..23); # _Zerinvary Lajos_, Mar 28 2007
%t Numerator[Table[Sum[1/k!,{k,1,n}],{n,1,30}]]
%o (PARI) a(n) = numerator(sum(k=1, n, 1/k!)); \\ _Michel Marcus_, Jun 01 2018
%Y Cf. A061354, A061355 (denominator).
%K frac,nonn
%O 1,2
%A _Alexander Adamchuk_, Jun 30 2006
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