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A137989 Decimal expansion of the inverse of the number whose Engel expansion has the sequence of double factorial numbers (A000165) as coefficients.

%I A137989 #11 Feb 16 2025 08:33:07
%S A137989 3,7,1,8,9,6,7,8,6,2,4,4,2,5,5,8,4,7,8,3,9,5,5,1,5,3,1,1,0,6,8,3,4,0,
%T A137989 0,3,3,4,4,1,4,2,1,6,5,0,6,7,9,1,3,0,0,2,2,8,1,1,2,5,3,9,1,1,3,8,9,3,
%U A137989 4,8,3,0,4,4,4,1,7,6,7,7,6,4,3,0,9,3,0,2,6,3,3,1,0,7,2,5,3,6,5
%N A137989 Decimal expansion of the inverse of the number whose Engel expansion has the sequence of double factorial numbers (A000165) as coefficients.
%H A137989 G. C. Greubel, <a href="/A137989/b137989.txt">Table of n, a(n) for n = 0..5000</a>
%H A137989 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>.
%H A137989 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>.
%p A137989 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/w; print(evalf(1/a,100)); od; end: P(100);
%t A137989 RealDigits[N[(1/Sum[Product[1/((k - 1)!!), {k, 1, n}], {n, 1, 250}]), 100]][[1]] (* _G. C. Greubel_, Jan 01 2016 *)
%Y A137989 Cf. A000142, A137986, A137987, A137988.
%K A137989 easy,nonn,cons
%O A137989 0,1
%A A137989 _Paolo P. Lava_ and _Giorgio Balzarotti_, Feb 26 2008