A248676 Decimal expansion of r = sum_{n >= 0} floor(n/3)!/n!.

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

Offset: 1

Author

Clark Kimberling, Oct 11 2014

Keywords

• nonn
• easy
• cons

Examples

			r = 2.71990926549085383421322286522452521...
		

Links

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

Crossrefs

Cf. A248675, A248677, A248664.

Programs

Maple

evalf(sum(floor(n/3)!/n!, n=0..infinity),120); # Vaclav Kotesovec, Oct 17 2014

Mathematica

x = N[Sum[Floor[n/2]!/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248675 *)
x = N[Sum[Floor[n/3]!/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248676 *)
x = N[Sum[Floor[n/4]!/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248677 *)

Formula

r = sum_{n >= 0} p(3,n)*n!/(3*n + 2)!, where p(k,n) is defined at A248664.