A255169 Decimal expansion of the sum_{n>=0} n^2/e^n = e(1+e)/(e-1)^3.

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

Offset: 1

Author

Richard R. Forberg, Feb 15 2015

Keywords

• nonn
• cons

Comments

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!.

See A098875 for the first degree polynomial and value.

Examples

			1.99229476712498....
		

Crossrefs

Cf. A008292, A098875.

Programs

Mathematica

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

PARI

suminf(n=0, n^2/exp(n)) \\ Michel Marcus, Jul 30 2018

PARI

exp(1)*(1+exp(1))/(exp(1)-1)^3 \\ Altug Alkan, Jul 30 2018

Formula

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