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A088694 E.g.f: A(x) = f(x*A(x)^3), where f(x) = (1+4*x)*exp(x). 0

%I

%S 1,5,159,10228,1009253,135069696,22882888555,4696799559488,

%T 1133128780421385,314294095403352064,98550149514670698071,

%U 34473870245560804316160,13310522831484403851847981,5622806397207798234900070400,2579680348909056700728913816227

%N E.g.f: A(x) = f(x*A(x)^3), where f(x) = (1+4*x)*exp(x).

%C Radius of convergence of A(x): r = (3^2/4^4)*exp(-1/4) = 0.0273797..., where A(r) = (4/3)*exp(1/12) and r = limit a(n)/a(n+1)*(n+1) as n->infinity. Radius of convergence is from a general formula yet unproved.

%F a(n) = n! * [x^n] ((1+4*x)*exp(x))^(3*n+1)/(3*n+1).

%F a(n) ~ 16^(2*n+1) * n^(n-1) / (sqrt(13) * 9^(n+1) * exp(3*n/4 - 1/12)). - _Vaclav Kotesovec_, Jan 24 2014

%t Table[n!*SeriesCoefficient[((1+4*x)*E^x)^(3*n+1)/(3*n+1),{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jan 24 2014 *)

%o (PARI) a(n)=n!*polcoeff(((1+4*x)*exp(x))^(3*n+1)+x*O(x^n),n,x)/(3*n+1)

%Y Cf. A088690, A088692, A088693.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 07 2003

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)