%I A038048
%S A038048 1,3,8,42,144,1440,5760,75600,524160,6531840,43545600,1117670400,
%T A038048 6706022400,149448499200,2092278988800,40537905408000,376610217984000,
%U A038048 13871809695744000,128047474114560000,5109094217170944000
%N A038048 a(n) = (n-1)! * sum {d|n} d.
%C A038048 Or, a(n) = Sum_{ d divides n } n!/d. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Jul 24 2005
%C A038048 Number of labeled regular octopi (or octopuses, cycles of ordered sets 
               all the same size).
%D A038048 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like 
               Structures, Camb. 1998, p. 56 (1.4.67).
%D A038048 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 159, #10, A(n,1).
%H A038048 T. D. Noe, <a href="b038048.txt">Table of n, a(n) for n=1..100</a>
%H A038048 H. Ochiai, <a href="http://arXiv.org/abs/math-ph/9909023">Counting functions 
               for branched covers of elliptic curves and quasi-modular forms</a>
%F A038048 a(p) = (p+1)*(p-1)! if p is a prime. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Jul 24 2005
%F A038048 E.g.f.: log(f(x)), where f(x) = o.g.f. for partitions (A000041), Product_{k=1..inf} 
               1/(1-x^k) - N. J. A. Sloane (njas(AT)research.att.com).
%F A038048 E.g.f.: Sum_{k>0} x^k/(k*(1-x^k)). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Mar 27 2005
%e A038048 a(6) = 6!{1/1 +1/2 +1/3 + 1/6}=1440.
%p A038048 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)
%Y A038048 Left edge of triangle in A008298. Cf. A058892.
%Y A038048 Cf. A057625.
%Y A038048 Cf. A110373, A110374.
%Y A038048 Sequence in context: A007175 A152394 A128322 this_sequence A051763 A074435 
               A039647
%Y A038048 Adjacent sequences: A038045 A038046 A038047 this_sequence A038049 A038050 
               A038051
%K A038048 easy,nonn,nice
%O A038048 1,2
%A A038048 Christian G. Bower (bowerc(AT)usa.net)
%E A038048 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 24 2005
%E A038048 Edited by N. J. A. Sloane (njas(AT)research.att.com), May 12 2008 at 
               the suggestion of Joerg Arndt.