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 A038048 a(n) = (n-1)! * sigma(n). 21
 1, 3, 8, 42, 144, 1440, 5760, 75600, 524160, 6531840, 43545600, 1117670400, 6706022400, 149448499200, 2092278988800, 40537905408000, 376610217984000, 13871809695744000, 128047474114560000, 5109094217170944000 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified April 10 22:35 EDT 2021. Contains 342862 sequences. (Running on oeis4.)