A124214 - OEIS

A124214

E.g.f.: exp(x) / (2 - exp(3*x))^(1/3).

1, 2, 10, 98, 1402, 26162, 601930, 16462658, 521659162, 18791451602, 758345497450, 33889063202018, 1661229537252922, 88627461127536242, 5112116659677605770, 317007674364657538178, 21030558126242472270682

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OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..350

FORMULA

a(n) ~ Gamma(2/3)*3^(n+1/2)*n^(n-1/6)/(sqrt(2*Pi)*exp(n)*(log(2))^(n+1/3)). - Vaclav Kotesovec, Jun 26 2013

E.g.f. A(x) satisfies: A'(x) = A(x) + A(x)^4. - Paul D. Hanna, Dec 18 2013

E.g.f. A(x) satisfies: A(x) = exp(x + Integral A(x)^3 dx) with A(0)=1. - Paul D. Hanna, Dec 18 2013

a(n) = 2^(-1/3) * Sum_{k >= 0} (1/18)^k*A004987(k)*(3*k + 1)^n = 2^(-1/3) * Sum_{k >= 0} (-1/2)^k*binomial(-1/3, k)*(3*k + 1)^n. Cf. A124212 and A229558. - Peter Bala, Aug 30 2016

MAPLE

A124214 := proc(n)

exp(x)/root[3](2-exp(3*x)) ;

coeftayl(%, x=0, n)*n! ;

end proc: # R. J. Mathar, Dec 19 2013

MATHEMATICA

CoefficientList[Series[Exp[x]/(2-Exp[3*x])^(1/3), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)

PROG

(PARI) a(n)=local(A=1+x); for(i=1, n, A=1+intformal(A+A^4+x*O(x^n))); n!*polcoeff(A, n)

for(n=0, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Dec 18 2013

CROSSREFS

Cf. A229558, A004987, A124212.