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%I #32 Feb 26 2022 10:52:06
%S 1,1,1,-3,-15,-23,177,1253,1057,-37103,-245471,371085,15691665,
%T 76436089,-608056239,-10302629131,-20287425215,856245051169,
%U 8821231566145,-29959421725155,-1376333505095631,-7591883371988471,139148719952772849
%N Expansion of e.g.f.: exp(sin(x)*cos(x)).
%H Vincenzo Librandi, <a href="/A009210/b009210.txt">Table of n, a(n) for n = 0..125</a>
%F a(n) = sum(j=0..(n-1)/2, (2^(4*j-n+1)*sum(i=0..(n-2*j)/2,(2*i+2*j-n)^n*binomial(n-2*j,i)*(-1)^(n-j-i))/(n-2*j)!), n>0, a(0)=1. - _Vladimir Kruchinin_, May 29 2011
%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * (-4)^k * a(n-2*k-1). - _Ilya Gutkovskiy_, Feb 24 2022
%t With[{nn=30},CoefficientList[Series[Exp[Sin[x]*Cos[x]],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Aug 10 2021 *)
%o (Maxima)
%o a(n):=sum((2^(4*j-n+1)*sum((2*i+2*j-n)^n*binomial(n-2*j,i)*(-1)^(n-j-i),i,0,((n-2*j)/2)))/(n-2*j)!,j,0,((n-1)/2)); /* _Vladimir Kruchinin_, May 29 2011 */
%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(sin(x)*cos(x)))) /* _Joerg Arndt_, May 29 2011 */
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E Definition corrected by _Joerg Arndt_, May 29 2011
%E Definition clarified and prior Mathematica program replaced by _Harvey P. Dale_, Aug 10 2021
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