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%I #23 Apr 10 2022 02:39:28
%S 1,0,0,-1,0,1,10,-1,-56,-279,246,4619,14388,-53195,-556478,-864865,
%T 13276912,90192753,-72903378,-3987888493,-16957067028,101506932205,
%U 1411655530330,2206092853799,-70455418153496,-549095655588183,1428569363164230
%N Expansion of e.g.f.: exp(sin(x))/exp(x).
%F a(0) = 1; a(n) = Sum_{k=1..floor((n-1)/2)} (-1)^k * binomial(n-1,2*k) * a(n-2*k-1). - _Ilya Gutkovskiy_, Apr 09 2022
%t With[{nn=30},CoefficientList[Series[Exp[Sin[x]]/Exp[x],{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, Jun 27 2012 *)
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(sin(x))/exp(x))) \\ _Michel Marcus_, Apr 09 2022
%Y Cf. A002017, A009227.
%K sign,easy
%O 0,7
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E Definition clarified by _Harvey P. Dale_, Jun 27 2012
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