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A121860
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a(n) = Sum_{d|n} n!/(d!*(n/d)!).
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18
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1, 2, 2, 8, 2, 122, 2, 1682, 10082, 30242, 2, 7318082, 2, 17297282, 3632428802, 36843206402, 2, 2981705126402, 2, 1690185726028802, 3379030566912002, 28158588057602, 2, 76941821303636889602, 1077167364120207360002
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OFFSET
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1,2
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COMMENTS
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a(n) = 2 for prime n. It appears that all terms belong to A100195 (Numbers n such that the denominator of BernoulliB[n] is a record). - Alexander Adamchuk, Sep 09 2006
a(n) = 2 iff n is prime.
Number of matrices whose entries are 1,...,n, up to row and column permutations. For example, inequivalent representatives of the a(4) = 8 matrices are:
[1 2 3 4]
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[1 2] [1 2] [1 3] [1 3] [1 4] [1 4]
[3 4] [4 3] [2 4] [4 2] [2 3] [3 2]
.
[1]
[2]
[3]
[4]
(End)
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LINKS
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FORMULA
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E.g.f.: Sum_{k>0} (exp(x^k)-1)/k!.
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MATHEMATICA
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f[n_] := Block[{d = Divisors@n}, Plus @@ (n!/(d! (n/d)!))]; Array[f, 25] (* Robert G. Wilson v, Sep 11 2006 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, n!/(d!*(n/d)!)); \\ Michel Marcus, Sep 13 2018
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CROSSREFS
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KEYWORD
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easy,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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