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A258817
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a(n) = (!0 + !1 +... + !(n-1)) mod n.
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1
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0, 1, 2, 0, 3, 3, 0, 0, 8, 5, 4, 0, 9, 7, 8, 0, 13, 9, 4, 0, 14, 11, 14, 0, 3, 13, 17, 0, 25, 15, 4, 0, 26, 17, 28, 0, 30, 19, 35, 0, 4, 21, 9, 0, 8, 23, 32, 0, 7, 25, 47, 0, 30, 27, 48, 0, 23, 29, 45, 0, 48, 31, 35, 0, 48, 33, 12, 0, 14, 35, 7, 0, 34, 37, 53
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OFFSET
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1,3
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COMMENTS
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!n is a subfactorial number (A000166).
Property of the sequence: a(1) = a(7) = 0 and a(4k) = 0 for k=1,2,...
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LINKS
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FORMULA
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EXAMPLE
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a(5)= 3 because !0 + !1 + !2 + !3 + !4 = 1 + 0 + 1 + 2 + 9 = 13 == 3 mod 5.
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MAPLE
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A:= proc(n) option remember; if n<=1 then 1-n else (n-1)*(procname(n-1)+procname(n-2)); fi; end;
a:=n->n!*sum((-1)^k/k!, k=0..n):
lf:=n->add(A(k), k=0..n-1); [seq(lf(n) mod n, n=1..40)];
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MATHEMATICA
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Table[Mod[Total[Subfactorial[Range[0, n-1]]], n], {n, Range[80]}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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