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A137988 Decimal expansion of the number whose Pierce expansion has the sequence of double factorial numbers (A000165) as coefficients.

%I A137988 #11 Feb 16 2025 08:33:07
%S A137988 3,5,2,8,0,6,4,3,8,1,0,6,6,5,0,0,3,6,4,6,2,1,2,3,6,0,5,3,1,0,7,3,0,0,
%T A137988 8,6,3,1,1,1,4,5,9,6,9,4,4,4,9,9,0,1,7,4,0,2,7,4,9,4,6,3,1,0,7,1,8,6,
%U A137988 4,7,0,1,5,3,3,6,5,6,5,4,4,1,4,5,6,9,0,9,1,8,9,6,0,9,4,8,3,3,9
%N A137988 Decimal expansion of the number whose Pierce expansion has the sequence of double factorial numbers (A000165) as coefficients.
%H A137988 G. C. Greubel, <a href="/A137988/b137988.txt">Table of n, a(n) for n = 0..5000</a>
%H A137988 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>.
%H A137988 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>.
%p A137988 P:=proc(n) local a,i,j,k,w; a:=0; w:=1; for i from 0 by 1 to n do k:=i; j:=i-2; while j>0 do k:=k*j; j:=j-2; od; if (i=0 or i=1) then k:=1; fi; if i=2 then k:=2; fi; w:=w*k; a:=a+(-1)^i/w; print(evalf(a,100)); od; end: P(100);
%t A137988 RealDigits[N[(Sum[(-1)^n*Product[1/((k + 1)!!), {k, 1, n}], {n, 1, 250}]), 100]][[1]] (* _G. C. Greubel_, Jan 01 2017 *)
%Y A137988 Cf. A000142, A137986, A137987, A137989.
%K A137988 easy,nonn,cons
%O A137988 0,1
%A A137988 _Paolo P. Lava_ and _Giorgio Balzarotti_, Feb 26 2008