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A137986 Decimal expansion of the number whose Pierce expansion has the sequence of factorial numbers (A000142) as coefficients.

%I A137986 #12 Feb 16 2025 08:33:07
%S A137986 4,2,0,1,0,9,9,9,3,8,8,3,4,8,7,3,4,1,7,6,1,6,5,4,5,3,7,9,4,0,0,0,9,0,
%T A137986 3,5,9,2,8,9,1,1,2,4,7,2,1,8,6,2,5,2,4,2,0,7,4,4,5,2,5,0,5,2,5,3,8,3,
%U A137986 5,1,0,1,5,3,7,8,1,3,5,8,7,7,5,6,1,5,3,4,7,1,0,3,5,8,4,1,9,4,5
%N A137986 Decimal expansion of the number whose Pierce expansion has the sequence of factorial numbers (A000142) as coefficients.
%H A137986 G. C. Greubel, <a href="/A137986/b137986.txt">Table of n, a(n) for n = 0..5000</a>
%H A137986 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>.
%H A137986 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>.
%p A137986 P:=proc(n) local a,i,k; a:=0; k:=1; for i from 0 by 1 to n do k:=k*i!; a:=a+(-1)^i/k; print(evalf(a,100)); od; end: P(100);
%t A137986 RealDigits[N[(Sum[(-1)^n*Product[1/((k - 1)!), {k, 1, n}], {n, 1, 250}]), 100]][[1]] (* _G. C. Greubel_, Jan 01 2017 *)
%Y A137986 Cf. A000142, A137987, A137988, A137989.
%K A137986 easy,nonn,cons
%O A137986 0,1
%A A137986 _Paolo P. Lava_ and _Giorgio Balzarotti_, Feb 26 2008