A207326 E.g.f. satisfies 2*A(x)-exp(A(x))+1=sin(x).
1, 1, 3, 22, 197, 2248, 31311, 514592, 9750137, 209265504, 5018169035, 132971582976, 3858414981085, 121679533902592, 4143895711622327, 151566138479037952, 5925617619735873969
Offset: 1
Keywords
Programs
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Mathematica
Rest[CoefficientList[Series[(-1 - 2*LambertW[-E^((Sin[x]-1)/2)/2] + Sin[x])/2,{x,0,20}],x] * Range[0,20]!] (* Vaclav Kotesovec, Aug 04 2014 *)
Formula
a(n)=sum((m=0..(n-1)/2, v(n-2*m)*sum(i=0..(n-2*m)/2, (2*i+2*m-n)^n*binomial(n-2*m,i)*(-1)^(n+m-i)))/(2^(n-2*m-1)*(n-2*m)!)), v(n)=A000311(n).
a(n) ~ ((1-log(2))*log(2))^(1/4) * n^(n-1) / ((arcsin(2*log(2)-1))^(n-1/2) * exp(n)). - Vaclav Kotesovec, Aug 04 2014