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A227464 E.g.f. equals the series reversion of sin(x) / exp(x).

%I A227464 #7 Jan 10 2014 17:03:13
%S A227464 1,2,10,80,884,12480,214600,4352000,101696400,2690754560,79516330400,
%T A227464 2595903897600,92782304200000,3603511009280000,151115361757776000,
%U A227464 6805240665866240000,327547876406050976000,16780408888535285760000,911669878205463707200000
%N A227464 E.g.f. equals the series reversion of sin(x) / exp(x).
%F A227464 E.g.f. A(x) satisfies: A(x) = asin(x*exp(A(x))).
%F A227464 a(n) ~ 2^((n-1)/2) * exp(n*Pi/4) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Jan 10 2014
%e A227464 E.g.f.: A(x) = x + 2*x^2/2! + 10*x^3/3! + 80*x^4/4! + 884*x^5/5! + 12480*x^6/6! +...
%e A227464 where A( sin(x)/exp(x) ) = x.
%t A227464 Rest[CoefficientList[InverseSeries[Series[Sin[x]/E^x,{x,0,20}],x],x] * Range[0,20]!] (* _Vaclav Kotesovec_, Jan 10 2014 *)
%o A227464 (PARI) {a(n)=local(X=x+x*O(x^n));n!*polcoeff(serreverse(sin(X)/exp(X)), n)}
%o A227464 for(n=1,25,print1(a(n),", "))
%o A227464 (PARI) {a(n)=local(A=x); for(i=1,n,A=asin(x*exp(A+x*O(x^n)))); n!*polcoeff(A, n)}
%o A227464 for(n=1,25,print1(a(n),", "))
%Y A227464 Cf. A227463.
%K A227464 nonn
%O A227464 1,2
%A A227464 _Paul D. Hanna_, Jul 14 2013