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A343187 Decimal expansion of Sum_{k>=1} 1/af(k), where af is the alternating factorial.

%I A343187 #14 Jun 04 2021 07:54:22
%S A343187 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 A343187 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 A343187 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 A343187 Decimal expansion of Sum_{k>=1} 1/af(k), where af is the alternating factorial.
%e A343187 2.2644055179325317... = 1/1 + 1/1 + 1/5 + 1/19 + 1/101 +....
%p A343187 evalf(sum(1/sum((-1)^(k - i)*i!, i = 1 .. k), k = 1 .. infinity));
%o A343187 (PARI) f(n) = sum(k=0, n-1, (-1)^k*(n-k)!); \\ A005165
%o A343187 suminf(n=1, 1/f(n)) \\ _Michel Marcus_, Apr 07 2021
%Y A343187 Cf. A005165 (alternating factorial).
%K A343187 cons,nonn
%O A343187 1,1
%A A343187 _Andrzej Kukla_, Apr 07 2021