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%I #19 Oct 04 2017 15:40:08
%S 1,-4,36,-848,23824,-871872,44942912,-2860930816,213856723200,
%T -19099352929280,2010469524579328,-242177953175506944,
%U 32998102512641970176,-5069553933584348397568,870871673923373487243264
%N E.g.f. sin(x*cos(x)) (odd powers only)
%F a(n)=(-1)^(n)*sum(k=0..n, binomial(2*n+1,2*k+1)*((sum(i=0..k, (2*k+1-2*i)^(2*n-2*k)*binomial(2*k+1,i))))/(2^(2*k))). - _Vladimir Kruchinin_, Jun 18 2011
%t With[{nn=30},Take[CoefficientList[Series[Sin[x Cos[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Oct 04 2017 *)
%o (Maxima)
%o a(n):=(-1)^(n)*sum(binomial(2*n+1,2*k+1)*((sum((2*k+1-2*i)^(2*n-2*k)*binomial(2*k+1,i),i,0,((k)))))/(2^(2*k)),k,0,n); /* _Vladimir Kruchinin_, Jun 18 2011 */
%K sign
%O 0,2
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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