A248675 Decimal expansion of r = sum_{n >= 0} floor(n/2)!/n!.

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

Offset

1,1

Links

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

Formula

r = sum_{n >= 0} p(2,n)*n!/(2*n + 1)!, where p(k,n) is defined at A248664.

Example

r = 2.7768896094079797269812451636...

Maple

evalf(sum(floor(n/2)!/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. A248676, A248677, A248664.

Sequence in context: A230160 A063503 A244976 * A068386 A021040 A246553

Adjacent sequences: A248672 A248673 A248674 * A248676 A248677 A248678

Keyword

nonn,easy,cons

Author

Clark Kimberling, Oct 11 2014

Status

approved