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A227464
E.g.f. equals the series reversion of sin(x) / exp(x).
2
1, 2, 10, 80, 884, 12480, 214600, 4352000, 101696400, 2690754560, 79516330400, 2595903897600, 92782304200000, 3603511009280000, 151115361757776000, 6805240665866240000, 327547876406050976000, 16780408888535285760000, 911669878205463707200000
OFFSET
1,2
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
EXAMPLE
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.
MATHEMATICA
Rest[CoefficientList[InverseSeries[Series[Sin[x]/E^x, {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 10 2014 *)
PROG
(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), ", "))
CROSSREFS
Cf. A227463.
Sequence in context: A227463 A008544 A133480 * A269353 A064312 A063902
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 14 2013
STATUS
approved