A343187 - OEIS

%I #14 Jun 04 2021 07:54:22

%S 2,2,6,4,4,0,5,5,1,7,9,3,2,5,3,1,7,0,6,2,9,3,4,5,7,9,7,0,3,3,6,2,9,5,

%T 3,8,4,3,7,7,0,7,9,1,2,7,4,3,7,4,4,8,9,0,3,0,4,9,6,6,7,1,0,6,1,9,8,7,

%U 0,9,1,4,2,5,9,8,7,8,7,6,8,1,2,7,2,4,7,9,3,0,4,0,7,7,0,9,0,2,8,9,8,2,7,9,9

%N Decimal expansion of Sum_{k>=1} 1/af(k), where af is the alternating factorial.

%e 2.2644055179325317... = 1/1 + 1/1 + 1/5 + 1/19 + 1/101 +....

%p evalf(sum(1/sum((-1)^(k - i)*i!, i = 1 .. k), k = 1 .. infinity));

%o (PARI) f(n) = sum(k=0, n-1, (-1)^k*(n-k)!); \\ A005165

%o suminf(n=1, 1/f(n)) \\ _Michel Marcus_, Apr 07 2021

%Y Cf. A005165 (alternating factorial).

%K cons,nonn

%O 1,1

%A _Andrzej Kukla_, Apr 07 2021