%I #15 Jul 30 2018 22:57:05

%S 1,9,9,2,2,9,4,7,6,7,1,2,4,9,8,7,3,9,2,9,2,6,0,1,6,6,1,3,0,0,2,1,1,7,

%T 3,8,7,8,3,1,4,0,4,5,2,3,0,6,3,7,7,0,0,6,9,5,2,3,5,0,1,6,8,4,8,4,8,1,

%U 9,8,9,9,3,4,9,7,9,2,7,0,5,8

%N Decimal expansion of the sum_{n>=0} n^2/e^n = e(1+e)/(e-1)^3.

%C The expression generating this constant is a second degree Eulerian polynomial, in the "variable" e, with coefficients {1, 1}, generated from sum_{n>=0} n^m/e^n, with m=2. See A008292. It approximates m!.

%C See A098875 for the first degree polynomial and value.

%F Equals sum_{n>=0} n^2/e^n.

%e 1.99229476712498....

%t Sum[n^2/Exp[n], {n, 0, Infinity}]; N[Sum[n^2/Exp[n], {n, 0, Infinity}],100]

%o (PARI) suminf(n=0, n^2/exp(n)) \\ _Michel Marcus_, Jul 30 2018

%o (PARI) exp(1)*(1+exp(1))/(exp(1)-1)^3 \\ _Altug Alkan_, Jul 30 2018

%Y Cf. A008292, A098875.

%K nonn,cons

%O 1,2

%A _Richard R. Forberg_, Feb 15 2015