A248685 Decimal expansion of r = sum{(floor(n/5)!)^5/n!, n >= 0}.

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

Offset: 1

Author

Clark Kimberling, Oct 11 2014

Keywords

• nonn
• easy
• cons

Examples

			r = 2.71829122423905735499923669685865...
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A248682, A248683, A248684, A248664.

Programs

Mathematica

x = N[Sum[(Floor[n/2])!^2/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248682 *)
x = N[Sum[(Floor[n/3])!^3/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248683 *)
x = N[Sum[(Floor[n/4])!^4/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248684 *)
x = N[Sum[(Floor[n/5])!^5/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248685 *)

Formula

r = sum{(n!^5)*p(5,n)/(5*n + 4)!, n >= 0}, where p(k,n) is defined at A248664.