OFFSET
0,3
FORMULA
a(n) ~ c * d^n, where d = 2.8333645039948803621658813720055524872119... and c = 0.1710130167563241590871776261530008679... - Vaclav Kotesovec, Jun 16 2022
a(n) = [q^n] K_{k>=0} -q^k / ((q^(k + 1) - 2*q + 1)/(q - 1)), where K is Gauss's notation for continued fractions. - Peter Luschny, Jun 20 2022
MATHEMATICA
nmax = 40; CoefficientList[Series[1/(1 - x/(1 - x + ContinuedFractionK[-x^k, 1 - x*(1 - x^k)/(1 - x), {k, 2, nmax}])), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 16 2022 *)
A355040List[nmax_] := Module[{a, b, q},
a = ContinuedFractionK[-q^k, (q^(k + 1) - 2 q + 1)/(q - 1), {k, 0, nmax}];
b = Series[a, {q, 0, nmax}]; CoefficientList[b, q] ];
A355040List[32] (* Peter Luschny, Jun 20 2022 *)
PROG
(PARI) N=44; q='q+O('q^N);
f(n) = 1 - sum(k=1, n-1, q^k);
s=1; forstep(j=N, 1, -1, s = q^j/s; s = f(j) - s ); s = 1/s;
Vec(s)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jun 16 2022
STATUS
approved