cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A309087 a(n) = Sum_{k >= 0} floor(n^k / k!).

Original entry on oeis.org

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

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Author

Rémy Sigrist, Jul 11 2019

Keywords

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.

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.
		

Crossrefs

See A309103, A309104, A309105 for similar sequences.

Programs

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

Formula

a(n) ~ exp(n) as n tends to infinity.
a(n) <= A000149(n).
a(n) = A309104(n) + A309105(n).
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