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%I #26 Jan 22 2018 03:05:01
%S 0,1,-1,2,-8,31,-136,692,-3968,25261,-176896,1351382,-11184128,
%T 99680491,-951878656,9695756072,-104932671488,1202439837721,
%U -14544442556416,185185594118762,-2475749026562048,34674437196568951
%N Expansion of e.g.f.: sinh(log(1 + sin(x))).
%C |a(n)| = number of odd alternating permutations on n letters (offset 1). - _Vladeta Jovovic_, May 20 2007
%H G. C. Greubel, <a href="/A009567/b009567.txt">Table of n, a(n) for n = 0..450</a>
%F a(2*n) = A000182(n+1)/2.
%F a(2*n+1) = A012007(n+1) - 1.
%t With[{nn=30},CoefficientList[Series[Sinh[Log[1+Sin[x]]],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, May 11 2014 *)
%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(sinh(log(1+sin(x)))))) \\ _G. C. Greubel_, Jan 21 2018
%Y Cf. A000111, A009123.
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E Definition clarified and previous Mathematica program replaced by _Harvey P. Dale_, May 11 2014