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

1, 1, 3, 18, 150, 1590, 20580, 314790, 5554710, 111071520, 2482076520, 61301435580, 1658129152680, 48749053413060, 1547849157554700, 52785934927525800, 1924269399236784600, 74672595203551745400, 3073314600152521124400, 133716009695044269893400, 6132253708189762323370200

Offset

1,3

Links

Table of n, a(n) for n=1..21.

Formula

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

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

Example

E.g.f.: A(x) = x + x^2/2! + 3*x^3/3! + 18*x^4/4! + 150*x^5/5! +...
where A(1+x - exp(x^2/2)) = x and A(x) = x-1 + exp(A(x)^2/2).

Mathematica

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

Prog

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

Crossrefs

Cf. A200319, A213641, A030178.

Sequence in context: A221961 A138420 A152409 * A352850 A347020 A371538

Adjacent sequences: A200317 A200318 A200319 * A200321 A200322 A200323

Keyword

nonn

Author

Paul D. Hanna, Nov 15 2011

Status

approved