A309087 a(n) = Sum_{k >= 0} floor(n^k / k!).
1, 2, 6, 18, 50, 143, 397, 1088, 2973, 8093, 22014, 59861, 162742, 442396, 1202589, 3268996, 8886090, 24154933, 65659949, 178482278, 485165168, 1318815708, 3584912818, 9744803414, 26489122097, 72004899306, 195729609397, 532048240570, 1446257064252
Offset: 0
Keywords
Examples
For n = 3: - we have: k floor(3^k / k!) - --------------- 0 1 1 3 2 4 3 4 4 3 5 2 6 1 >=7 0 - hence a(3) = 1 + 3 + 4 + 4 + 3 + 2 + 1 = 18.
Links
- Wikipedia, Taylor series: Exponential function
Programs
-
PARI
a(n) = { my (v=0, d=1); for (k=1, oo, if (d<1, return (v), v += floor(d); d *= n/k)) }
Comments