OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f.: 1/(3 - E(0)), where E(k)= 1 + 2^k/(1 - x/(x + 2^k*(k+1)/E(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 21 2013
a(n) ~ 2*n!/((13-sqrt(13))*(log((sqrt(13)-1)/2))^(n+1)). - Vaclav Kotesovec, Aug 13 2013
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (2^k + 1) * a(n-k). - Ilya Gutkovskiy, Jan 15 2020
MAPLE
seq(coeff(series(factorial(n)*(3-exp(x)-exp(2*x))^(-1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 10 2018
MATHEMATICA
With[{nn=20}, CoefficientList[Series[1/(3-Exp[x]-Exp[2x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 04 2011 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(1/(3-sum(k=1, 2, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(3-Exp(x)-Exp(2*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved