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

1, 2, 10, 80, 884, 12480, 214600, 4352000, 101696400, 2690754560, 79516330400, 2595903897600, 92782304200000, 3603511009280000, 151115361757776000, 6805240665866240000, 327547876406050976000, 16780408888535285760000, 911669878205463707200000

Offset: 1

Author

Paul D. Hanna, Jul 14 2013

Keywords

• nonn

Examples

			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! +...
where A( sin(x)/exp(x) ) = x.
		

Crossrefs

Cf. A227463.

Programs

Mathematica

Rest[CoefficientList[InverseSeries[Series[Sin[x]/E^x,{x,0,20}],x],x] * Range[0,20]!] (* Vaclav Kotesovec, Jan 10 2014 *)

PARI

{a(n)=local(X=x+x*O(x^n));n!*polcoeff(serreverse(sin(X)/exp(X)), n)}
for(n=1,25,print1(a(n),", "))

PARI

{a(n)=local(A=x); for(i=1,n,A=asin(x*exp(A+x*O(x^n)))); n!*polcoeff(A, n)}
for(n=1,25,print1(a(n),", "))

Formula

E.g.f. A(x) satisfies: A(x) = asin(x*exp(A(x))).

a(n) ~ 2^((n-1)/2) * exp(n*Pi/4) * n^(n-1) / exp(n). - Vaclav Kotesovec, Jan 10 2014