A038048 a(n) = (n-1)! * sigma(n).

1, 3, 8, 42, 144, 1440, 5760, 75600, 524160, 6531840, 43545600, 1117670400, 6706022400, 149448499200, 2092278988800, 40537905408000, 376610217984000, 13871809695744000, 128047474114560000, 5109094217170944000

Offset

1,2

Comments

sigma(n) = A000203(n) is the sum of the divisors of n.

Number of labeled regular octopi (or octopuses, cycles of ordered sets all the same size).

Left edge of triangle in A008298.

References

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 56 (1.4.67).

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 159, #10, A(n,1).

Links

T. D. Noe, Table of n, a(n) for n = 1..100

Xiaojun Liu, Motohico Mulase, Adam Sorkin, Quantum curves for simple Hurwitz numbers of an arbitrary base curve, arXiv:1304.0015 [math.AG], 2013.

H. Ochiai, Counting functions for branched covers of elliptic curves and quasi-modular forms, arXiv:math-ph/9909023, 1999.

Formula

a(n) = Sum_{d|n} n!/d. - Amarnath Murthy, Jul 24 2005

a(p) = (p+1)*(p-1)! if p is a prime. - Amarnath Murthy, Jul 24 2005

E.g.f.: log(f(x)), where f(x) = o.g.f. for partitions (A000041), Product_{k>=1} 1/(1 - x^k). - N. J. A. Sloane

E.g.f.: Sum_{k>0} x^k/(k*(1-x^k)). - Vladeta Jovovic, Mar 27 2005

a(n) = A000142(n-1)*A000203(n). - Omar E. Pol, Feb 26 2014

Example

a(6) = 5! * (1 + 2 + 3 + 6) = 1440 = 6! * (1 + 1/2 + 1/3 + 1/6).

Maple

a := n -> n!*add(1/j, j=numtheory:-divisors(n)): seq(a(n), n=1..23); # Emeric Deutsch, Jul 24 2005

Mathematica

a[n_] := (n-1)!*DivisorSigma[1, n]; Table[a[n], {n, 20}] (* Jean-François Alcover, Mar 23 2011 *)

Prog

(PARI) a(n)=(n-1)!*sigma(n) \\ Charles R Greathouse IV, Mar 09 2014
(Sage)
A038048 = lambda n: factorial(n-1)*sigma(n, 1)
[A038048(n) for n in (1..20)] # Peter Luschny, Jan 19 2016

Crossrefs

Cf. A000203, A057625, A058892, A110373, A110374.

Sequence in context: A224246 A128322 A337758 * A051763 A074435 A039647

Adjacent sequences: A038045 A038046 A038047 * A038049 A038050 A038051

Keyword

nonn,nice,easy

Author

Christian G. Bower

Extensions

More terms from Emeric Deutsch, Jul 24 2005

Edited by N. J. A. Sloane, May 12 2008 at the suggestion of Joerg Arndt

Status

approved