cp's OEIS Frontend

A252848 Decimal expansion of Sum_{n>0} Sum_{k=0..n} exp(k)/n! = e*(e^e - 1)/(e - 1).

%I A252848 #14 Dec 24 2014 23:08:34
%S A252848 2,2,3,9,1,7,1,3,1,6,8,9,4,0,2,1,7,1,1,4,4,1,3,7,7,6,9,6,3,8,8,1,7,3,
%T A252848 1,3,2,4,9,9,2,1,6,7,2,3,3,4,4,5,1,9,4,4,7,2,8,5,1,0,9,9,1,7,2,7,9,0,
%U A252848 6,8,9,3,4,4,9,9,8,0,5,6,1,0
%N A252848 Decimal expansion of Sum_{n>0} Sum_{k=0..n} exp(k)/n! = e*(e^e - 1)/(e - 1).
%C A252848 Terms in the sum begin:  1 + (1 + e)/1 + (1 + e + e^2)/2 + (1 + e + e^2 + e^3)/6 + ... .
%C A252848 The largest term in the sum is at n = 2, where that term is 5.5536... .
%C A252848 The double sum converges to a similar algebraic form using any base for exponentiation. For instance, using Pi as the base shows the general closed form:
%C A252848 Pi*(e^Pi - e)/(Pi - 1), which equals 29.9584963... .
%C A252848 As the base approaches 1, the ratio converges to 2e = Sum_{n>0} Sum_{k=0..n} 1/n! = 5.43656... . See A019762.
%F A252848 e*(e^e - 1)/(e - 1).
%e A252848 22.391713168940217114413... .
%t A252848 Sum[N[Sum[Exp[k]/n!, {k, 0, n}], 100], {n, 0, Infinity}]
%K A252848 nonn,cons
%O A252848 2,1
%A A252848 _Richard R. Forberg_, Dec 22 2014