A248677 Decimal expansion of r = sum_{n >= 0} floor(n/4)!/n!.

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

Offset

1,1

Links

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

Formula

r = sum_{n >= 0} p(4,n)*n!/(4*n + 3)!, where p(k,n) is defined at A248664.

Example

r = 2.718309697707245618330408276361873...

Maple

evalf(sum(floor(n/4)!/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 *)

Crossrefs

Cf. A248675, A248676, A248664.

Sequence in context: A368653 A248685 A182587 * A198128 A094121 A105178

Adjacent sequences: A248674 A248675 A248676 * A248678 A248679 A248680

Keyword

nonn,easy,cons

Author

Clark Kimberling, Oct 11 2014

Status

approved