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 A121860 a(n) = Sum_{d|n} n!/(d!*(n/d)!). 6

%I

%S 1,2,2,8,2,122,2,1682,10082,30242,2,7318082,2,17297282,3632428802,

%T 36843206402,2,2981705126402,2,1690185726028802,3379030566912002,

%U 28158588057602,2,76941821303636889602,1077167364120207360002

%N a(n) = Sum_{d|n} n!/(d!*(n/d)!).

%C 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

%C a(n) = 2 iff n is prime.

%C a(468) has 1007 decimal digits. - _Michael De Vlieger_, Sep 12 2018

%C From _Gus Wiseman_, Jan 10 2019: (Start)

%C 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:

%C [1 2 3 4]

%C .

%C [1 2] [1 2] [1 3] [1 3] [1 4] [1 4]

%C [3 4] [4 3] [2 4] [4 2] [2 3] [3 2]

%C .

%C [1]

%C [2]

%C [3]

%C [4]

%C (End)

%H Michael De Vlieger, <a href="/A121860/b121860.txt">Table of n, a(n) for n = 1..467</a>

%H Jimmy Devillet, Gergely Kiss, <a href="https://arxiv.org/abs/1806.02073">Characterizations of biselective operations</a>, arXiv:1806.02073 [math.RA], 2018.

%F E.g.f.: Sum_{k>0} (exp(x^k)-1)/k!.

%t f[n_] := Block[{d = Divisors@n}, Plus @@ (n!/(d! (n/d)!))]; Array[f, 25] (* _Robert G. Wilson v_, Sep 11 2006 *)

%t Table[DivisorSum[n, n!/(#!*(n/#)!) &], {n, 25}] (* _Michael De Vlieger_, Sep 12 2018 *)

%o (PARI) a(n) = sumdiv(n, d, n!/(d!*(n/d)!)); \\ _Michel Marcus_, Sep 13 2018

%Y Cf. A038041, A057625, A061095, A100195, A236696, A320444.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Sep 09 2006

%E More terms from _Robert G. Wilson v_, Sep 11 2006

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Last modified December 13 09:54 EST 2019. Contains 329968 sequences. (Running on oeis4.)