A207326 - OEIS

%I #8 Aug 04 2014 07:31:11

%S 1,1,3,22,197,2248,31311,514592,9750137,209265504,5018169035,

%T 132971582976,3858414981085,121679533902592,4143895711622327,

%U 151566138479037952,5925617619735873969

%N E.g.f. satisfies 2*A(x)-exp(A(x))+1=sin(x)

%F 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).

%F 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

%t 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 *)

%K nonn

%O 1,3

%A _Vladimir Kruchinin_, Feb 17 2012