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%I #10 Jun 16 2022 11:28:11
%S 1,1,2,4,9,21,50,121,296,730,1811,4513,11285,28294,71088,178904,
%T 450840,1137345,2871720,7256093,18345060,46403039,117421762,297232446,
%U 752601692,1906056161,4828267801,12232594912,30996034963,78549710061,199079279640,504596195477,1279065489044
%N Expansion of the continued fraction 1 / (1-q-q^2 / (1-q-q^2-q^3 / (1-q-q^2-q^3-q^4 / (...))))
%C Starts similar to A091964, terms differ after 730.
%F a(n) ~ c * d^n, where d = 2.5358790673564851880281667369326354455... and c = 0.14917782209027525483339419811881753... - _Vaclav Kotesovec_, Jun 16 2022
%t nmax = 40; CoefficientList[Series[1/(1 - x - x^2/(1 - x - x^2 + ContinuedFractionK[-x^k, 1 - x*(1 - x^k)/(1 - x), {k, 3, nmax}])), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 16 2022 *)
%o (PARI) N=44; q='q+O('q^N);
%o f(n) = 1 - sum(k=1,n-1,q^k);
%o s=1; forstep(j=N, 2, -1, s = q^j/s; s = f(j) - s ); s = 1/s;
%o Vec(s)
%Y Cf. A355040, A355046, A091964.
%K nonn
%O 0,3
%A _Joerg Arndt_, Jun 16 2022