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
Examples
r = 2.7768896094079797269812451636...
Links
- Clark Kimberling, Table of n, a(n) for n = 1..1000
Programs
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Maple
evalf(sum(floor(n/2)!/n!, n=0..infinity),120); # Vaclav Kotesovec, Oct 17 2014
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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(2,n)*n!/(2*n + 1)!, where p(k,n) is defined at A248664.