cp's OEIS Frontend

A098875 Decimal expansion of Sum_{n>0} n/exp(n).

%I A098875 #28 Jul 22 2024 03:12:48
%S A098875 9,2,0,6,7,3,5,9,4,2,0,7,7,9,2,3,1,8,9,4,5,4,1,3,5,2,2,7,1,6,4,9,9,6,
%T A098875 0,2,8,8,1,6,5,5,6,2,6,6,5,0,5,5,1,1,5,2,3,5,3,9,6,0,4,0,9,7,2,2,0,4,
%U A098875 7,1,9,7,4,6,5,0,2,4,4,5,6,8,6,7,3,6,9,9,7,3,2,8,3,4,3,4,7,9,4,7,2,5,3,9,7
%N A098875 Decimal expansion of Sum_{n>0} n/exp(n).
%C A098875 The expression generating this constant is a first degree Eulerian polynomial, in the "variable" e, with coefficient  {1}, generated from sum_{n>=0} n^m/e^n, with m=1.  See A008292. It approximates m!. - _Richard R. Forberg_, Feb 15 2015
%C A098875 See A255169 for the second degree polynomial and value.
%F A098875 Equals exp(1)/(exp(1)-1)^2.
%F A098875 From _Gleb Koloskov_, Jul 12 2021: (Start)
%F A098875 Equals (1/2)/(cosh(1)-1).
%F A098875 Equals 1+Sum_{n>0} B(2*n)*(1-2*n)/(2*n)! = 1+Sum_{n>0} (A027641(2*n)/A027642(2*n))*A165747(n)/A010050(n).
%F A098875 Equals LambertW(x)*LambertW(-1,x), where x = (1/(1-e))*exp(1/(1-e)) = -A073333*exp(-A073333). (End)
%e A098875 0.9206735942077923189454135227164996028816556266505511523539604097220...
%p A098875 g:=x->sum(n/exp(n),n=1..x); evalf[110](g(1500)); evalf[110](g(4000));
%t A098875 RealDigits[E/(E-1)^2, 10, 105][[1]] (* _Jean-François Alcover_, Jan 28 2014 *)
%o A098875 (PARI) 1+sumalt(n=1,bernreal(2*n)*(1-2*n)/(2*n)!) \\ _Gleb Koloskov_, Jul 12 2021
%Y A098875 Cf. A001113, A008292, A010050, A027641, A027642, A073333, A165747, A255169.
%K A098875 cons,nonn
%O A098875 0,1
%A A098875 Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 03 2004