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A038048
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(n-1)! * sigma(n).
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11
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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; internal format)
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OFFSET
| 1,2
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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).
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..100
H. Ochiai, Counting functions for branched covers of elliptic curves and quasi-modular forms
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FORMULA
| a(n) = Sum(d|n, n!/d). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 24 2005
a(p) = (p+1)*(p-1)! if p is a prime. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 24 2005
E.g.f.: log(f(x)), where f(x) = o.g.f. for partitions (A000041), Product(k=1..infinity, 1/(1-x^k)) - N. J. A. Sloane.
E.g.f.: Sum(k>0, x^k/(k*(1-x^k))). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 27 2005
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EXAMPLE
| a(6) = 5! * (1 + 2 + 3 + 6) = 1440.
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MAPLE
| with(numtheory): a:=proc(n) local div: div:=divisors(n): n!*sum(1/div[j], j=1..tau(n)) end: seq(a(n), n=1..23); (Deutsch)
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MATHEMATICA
| a[n_] := (n-1)!*DivisorSigma[1, n]; Table[a[n], {n, 20}] (* Jean-François Alcover, Mar 23 2011 *)
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CROSSREFS
| Cf. A058892, A057625, A000203, A110373, A110374.
Left edge of triangle in A008298.
Sequence in context: A152394 A168468 A128322 * A051763 A074435 A039647
Adjacent sequences: A038045 A038046 A038047 * A038049 A038050 A038051
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net)
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 24 2005
Edited by N. J. A. Sloane (njas(AT)research.att.com), May 12 2008 at the suggestion of Joerg Arndt.
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