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G.f.: 1 + C(1)*x/(1 + C(2)*x/(1 + C(3)*x/(1 + C(4)*x/(1 + C(5)*x/(1 +...))))), where C(n) are the Catalan numbers A000108.
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%I #13 Apr 16 2021 09:03:59

%S 1,1,-2,14,-238,10486,-1360142,566636294,-790250356798,

%T 3769300938094006,-62394920105801115182,3626853378943129415555174,

%U -747708300997964314376024192158,551445848326104642338923476399909526,-1465934793325188376367147565710854513799822,14139840911021914090289579305382872859520174083654

%N G.f.: 1 + C(1)*x/(1 + C(2)*x/(1 + C(3)*x/(1 + C(4)*x/(1 + C(5)*x/(1 +...))))), where C(n) are the Catalan numbers A000108.

%H Seiichi Manyama, <a href="/A343441/b343441.txt">Table of n, a(n) for n = 0..61</a>

%F G.f.: 1/(Sum_{k>=0} A268646(k) * (-x)^k).

%o (PARI) c(n) = binomial(2*n, n)/(n+1);

%o a(n) = my(A=1+O(x)); for(i=1, n, A=1+c(n-i+1)*x/A); polcoef(A, n);

%Y Cf. A000108, A268646.

%K sign

%O 0,3

%A _Seiichi Manyama_, Apr 15 2021