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A333892
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Number of permutations sigma of [n] such that i divides Product_{k=1..i} sigma(k) for 1 <= i <= n.
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2
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1, 1, 2, 4, 14, 36, 320, 1328, 7872, 51552, 756480, 5440752, 68999136, 584117952, 9632932800, 152699071104, 1881048314880, 21977611223040, 343998708042240, 4374197540536320, 77078374650869760, 1646804888482037760, 45052372505959096320, 727420047420178022400
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(5) = 36: 12345, 14325, 14352, 21345, 23145, 23415, 23451, 23541, 24315, 24351, 25341, 32145, 32415, 32451, 32541, 34125, 34152, 34215, 34251, 34512, 34521, 41325, 41352, 42315, 42351, 43125, 43152, 43215, 43251, 43512, 43521, 45312, 45321, 52341, 54312, 54321.
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MAPLE
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b:= proc(s) option remember; (n-> `if`(n=0, 1, `if`(irem(
mul(i, i=s), n)=0, add(b(s minus {j}), j=s), 0)))(nops(s))
end:
a:= n-> b({$1..n}):
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MATHEMATICA
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b[s_] := b[s] = With[{n = Length[s]}, If[n==0, 1, If[Mod[Times@@s, n]==0, Sum[b[s ~Complement~ {j}], {j, s}], 0]]];
a[n_] := b[Range[n]];
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PROG
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(PARI) {a(n) = if(n==0, 1, my(k=0); forperm([1..n], p, if(#Set(vector(n, i, prod(j=1, i, p[j])%i))==1, k++)); k)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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