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Expansion of 1/G(1) where G(k) = 1 - (q*(1+q))^k / G(k+1).
2

%I #9 Mar 01 2014 16:51:56

%S 1,1,2,4,10,23,54,131,319,773,1876,4570,11153,27230,66494,162420,

%T 396856,969918,2370885,5796072,14170603,34646935,84714724,207141788,

%U 506510118,1238559994,3028671297,7406137561,18110681635,44287420434,108299872576,264836004204,647630466817,1583719989406,3872845689552

%N Expansion of 1/G(1) where G(k) = 1 - (q*(1+q))^k / G(k+1).

%C What does this sequence count?

%F a(n) ~ c * d^n, where c = 0.2420970422648193730568648420401712... and d = 2.44542267258722345747732120775044... - _Vaclav Kotesovec_, Mar 01 2014

%o (PARI)

%o N = 66; q = 'q + O('q^N);

%o G(k) = if(k>N, 1, 1 - (q*(1+q))^k / G(k+1) );

%o Vec( 1/G(1) )

%Y Cf. A238435: 1/G(1) where G(k) = 1 - (q/(1-q))^k / G(k+1).

%Y Cf. A238437: 1/G(1) where G(k) = 1 - (q^k/(1-q^k)) / G(k+1).

%K nonn

%O 0,3

%A _Joerg Arndt_, Feb 27 2014