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A309103
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a(n) = Sum_{k >= 0} (-1)^k * floor(n^k / k!).
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1
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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
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OFFSET
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0,8
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(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)) }
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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