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A309103
a(n) = Sum_{k >= 0} (-1)^k * floor(n^k / k!).
1
1, 0, 0, 0, 0, -1, -1, -2, -1, -3, 0, 1, 0, -2, -1, -2, 2, 1, 1, 2, -2, 2, 0, -2, -3, 0, -1, -2, 0, -2, 3, -8, 1, -4, -3, -4, 1, -2, 1, -3, -2, -2, 2, 2, 3, 3, 2, 0, -5, -2, -3, -5, -2, -4, 3, 4, -2, -2, 4, -7, 3, 5, 3, 5, 0, -1, 1, -8, 6, -3, -1, 8, -5, 0, -6
OFFSET
0,8
COMMENTS
This sequence mimics the Maclaurin series for the function x -> exp(-x).
The series in the name is well defined; for any n > 0, only the first A065027(n) terms are different from zero.
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 = 0.
PROG
(PARI) a(n) = { my (v=0, d=1, s=+1); for (k=1, oo, if (d<1, return (v), v += s*floor(d); d *= n/k; s = -s)) }
CROSSREFS
See A309087 for similar sequences.
Cf. A065027.
Sequence in context: A062963 A143255 A127139 * A166139 A317367 A071431
KEYWORD
sign
AUTHOR
Rémy Sigrist, Jul 12 2019
STATUS
approved