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%I #22 Jun 24 2015 04:35:38
%S 0,1,-1,5,-24,134,-870,6474,-54432,510768,-5294160,60090480,
%T -741407040,9881421120,-141493322880,2166467990400,-35323552051200,
%U 611048958105600,-11178032634316800,215604729694771200,-4373272831527936000
%N Expansion of log(1+x)*cosh(log(1+x)).
%C |a(n)| = number of cycles in all permutations of [n] with odd number of cycles. - _Vladeta Jovovic_, Sep 06 2007
%C a(n) is a function of the harmonic numbers. - _Gary Detlefs_, Jul 13 2010
%H Robert Israel, <a href="/A009411/b009411.txt">Table of n, a(n) for n = 0..411</a>
%F a(n) = (-1)^(n+1)/2*(n!*H(n)-(n-2)!), n> 1, where H(n) = sum(1/k, k=1..n). - _Gary Detlefs_, Jul 13 2010
%p H:= n-> sum(1/k,k=1..n): seq((-1)^(n+1)/2*(n!*H(n)-(n-2)!),n = 2..20); # _Gary Detlefs_, Jul 13 2010
%t Log[ 1+x ]*Cosh[ Log[ 1+x ] ]
%Y Cf. A000254.
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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