OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..387
FORMULA
E.g.f.: 3 / (3 + exp(x) - exp(4*x)).
a(n) ~ n! * (r^3 - 1) * (4*r^3 - 16*r^2 + 64*r - 3) / (771 * log(r)^(n+1)), where r = 1.452626878833844... is the positive real root of the equation r*(r^3 - 1) = 3. - Vaclav Kotesovec, Aug 31 2020
MAPLE
E:= 3 / (3 + exp(x) - exp(4*x)):
S:= series(E, x, 41):
seq(n!*coeff(S, x, n), n=0..40); # Robert Israel, Oct 13 2020
MATHEMATICA
a[0] = 1; a[n_] := a[n] = (1/3) Sum[Binomial[n, k] (4^k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[3/(3 + Exp[x] - Exp[4 x]), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) seq(n)={Vec(serlaplace(3 / (3 + exp(x + O(x*x^n)) - exp(4*x + O(x*x^n)))))} \\ Andrew Howroyd, Aug 31 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 31 2020
STATUS
approved