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A200320 E.g.f. satisfies: A(x) = x-1 + exp(A(x)^2/2). 2

%I

%S 1,1,3,18,150,1590,20580,314790,5554710,111071520,2482076520,

%T 61301435580,1658129152680,48749053413060,1547849157554700,

%U 52785934927525800,1924269399236784600,74672595203551745400,3073314600152521124400,133716009695044269893400,6132253708189762323370200

%N E.g.f. satisfies: A(x) = x-1 + exp(A(x)^2/2).

%F E.g.f.: Series_Reversion(1+x - exp(x^2/2)).

%F a(n) ~ n^(n-1) * c^(n/2) / (sqrt(1+c) * exp(n) * (c-1+sqrt(c))^(n-1/2)), where c = LambertW(1) = 0.5671432904... (see A030178). - _Vaclav Kotesovec_, Jan 10 2014

%e E.g.f.: A(x) = x + x^2/2! + 3*x^3/3! + 18*x^4/4! + 150*x^5/5! +...

%e where A(1+x - exp(x^2/2)) = x and A(x) = x-1 + exp(A(x)^2/2).

%t Rest[CoefficientList[InverseSeries[Series[1 - E^(x^2/2) + x,{x,0,20}],x],x] * Range[0,20]!] (* _Vaclav Kotesovec_, Jan 10 2014 *)

%o (PARI) {a(n)=n!*polcoeff(serreverse(1+x-exp(x^2/2+x^2*O(x^n))),n)}

%Y Cf. A200319, A213641, A030178.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Nov 15 2011

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Last modified January 21 03:58 EST 2022. Contains 350473 sequences. (Running on oeis4.)