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

0,2

Comments

This sequence is inspired by the Maclaurin series for the exponential function.

The series in the name is well defined; for any n > 0, only the first A065027(n) terms are different from zero.

Links

Table of n, a(n) for n=0..28.

Wikipedia, Taylor series: Exponential function

Formula

a(n) ~ exp(n) as n tends to infinity.

a(n) <= A000149(n).

a(n) = A309104(n) + A309105(n).

Example

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.

Prog

(PARI) a(n) = { my (v=0, d=1); for (k=1, oo, if (d<1, return (v), v += floor(d); d *= n/k)) }

Crossrefs

See A309103, A309104, A309105 for similar sequences.

Cf. A000149, A065027.

Sequence in context: A180282 A081154 A002900 * A199770 A204322 A196593

Adjacent sequences: A309084 A309085 A309086 * A309088 A309089 A309090

Keyword

nonn

Author

Rémy Sigrist, Jul 11 2019

Status

approved