A057625 a(n) = n! * sum 1/k! where the sum is over all positive integers k that divide n.

1, 3, 7, 37, 121, 1201, 5041, 62161, 423361, 5473441, 39916801, 818959681, 6227020801, 130784734081, 1536517382401, 32256486662401, 355687428096001, 10679532671808001, 121645100408832001, 3770998783116364801, 59616236292028416001, 1686001119824999577601

Offset

1,2

Comments

Sets of lists of equal size, cf. A000262. - Vladeta Jovovic, Nov 02 2003

From Gus Wiseman, Jan 10 2019: (Start)

Number of matrices whose entries are 1,...,n, up to column permutations. For example, inequivalent representatives of the a(4) = 37 matrices are:

One 1 X 4 matrix:

[1234]

12 2 X 2 matrices:

[12] [12] [13] [13] [14] [14] [23] [23] [24] [24] [34] [34]

[34] [43] [24] [42] [23] [32] [14] [41] [13] [31] [12] [21]

and 24 4 X 1 matrices:

[1][1][1][1][1][1][2][2][2][2][2][2][3][3][3][3][3][3][4][4][4][4][4][4]

[2][2][3][3][4][4][1][1][3][3][4][4][1][1][2][2][4][4][1][1][2][2][3][3]

[3][4][2][4][2][3][3][4][1][4][1][3][2][4][1][4][1][2][2][3][1][3][1][2]

[4][3][4][2][3][2][4][3][4][1][3][1][4][2][4][1][2][1][3][2][3][1][2][1]

in total 1+12+24 = 37.

(End)

Links

Seiichi Manyama, Table of n, a(n) for n = 1..449

Formula

E.g.f.: Sum_{n>0} (exp(x^n)-1). - Vladeta Jovovic, Dec 30 2001

E.g.f.: Sum_{k>0} x^k/k!/(1-x^k). - Vladeta Jovovic, Oct 14 2003

Equals the logarithmic derivative of A209903. - Paul D. Hanna, Jul 26 2012

Example

a(4) = 4! (1 + 1/2! + 1/4!) = 24 (1 + 1/2 + 1/24) = 37.

Mathematica

a[n_] := n! DivisorSum[n, 1/#! &]; Array[a, 22] (* Jean-François Alcover, Dec 23 2015 *)

Prog

(PARI) a(n)=n! * sumdiv(n, d, 1/d! );  /* Joerg Arndt, Oct 07 2012 */

Crossrefs

Cf. A000005, A005225, A038041, A038048, A061095, A121860, A209903 (exp), A236696, A320444.

Row sums of A066387.

Sequence in context: A260378 A020463 A356668 * A308392 A087208 A161675

Adjacent sequences: A057622 A057623 A057624 * A057626 A057627 A057628

Keyword

nonn

Author

Leroy Quet, Oct 09 2000

Status

approved