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A015107 Carlitz-Riordan q-Catalan numbers (recurrence version) for q=-10.

%I A015107 #30 Nov 17 2019 09:30:38
%S A015107 1,1,-9,-919,917271,9174563561,-917438025443049,
%T A015107 -917439860513400673559,9174396770273536422744011031,
%U A015107 917439695376166450708460281823359721,-917439693541287252616828116888122637934368489
%N A015107 Carlitz-Riordan q-Catalan numbers (recurrence version) for q=-10.
%H A015107 Seiichi Manyama, <a href="/A015107/b015107.txt">Table of n, a(n) for n = 0..45</a>
%H A015107 Robin Sulzgruber, <a href="https://doi.org/10.25365/thesis.30616">The Symmetry of the q,t-Catalan Numbers</a>, Thesis, University of Vienna, 2013.
%F A015107 a(n+1) = Sum_{i=0..n} q^i*a(i)*a(n-i) with q=-10 and a(0)=1.
%F A015107 G.f. satisfies: A(x) = 1 / (1 - x*A(-10*x)) = 1/(1-x/(1+10*x/(1-10^2*x/(1+10^3*x/(1-...))))) (continued fraction). - _Seiichi Manyama_, Dec 28 2016
%e A015107 G.f. = 1 + x - 9*x^2 - 919*x^3 + 917271*x^4 + 9174563561*x^5 + ...
%t A015107 m = 11; ContinuedFractionK[If[i == 1, 1, -(-10)^(i-2) x], 1, {i, 1, m}] + O[x]^m // CoefficientList[#, x]& (* _Jean-François Alcover_, Nov 17 2019 *)
%o A015107 (Ruby)
%o A015107 def A(q, n)
%o A015107   ary = [1]
%o A015107   (1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + q ** j * ary[j] * ary[i - 1 - j]}}
%o A015107   ary
%o A015107 end
%o A015107 def A015107(n)
%o A015107   A(-10, n)
%o A015107 end # _Seiichi Manyama_, Dec 25 2016
%Y A015107 Cf. A227543.
%Y A015107 Cf. A015108 (q=-11), this sequence (q=-10), A015106 (q=-9), A015105 (q=-8), A015103 (q=-7), A015102 (q=-6), A015100 (q=-5), A015099 (q=-4), A015098 (q=-3), A015097 (q=-2), A090192 (q=-1), A000108 (q=1), A015083 (q=2), A015084 (q=3), A015085 (q=4), A015086 (q=5), A015089 (q=6), A015091 (q=7), A015092 (q=8), A015093 (q=9), A015095 (q=10), A015096 (q=11).
%Y A015107 Column k=10 of A290789.
%K A015107 sign
%O A015107 0,3
%A A015107 _Olivier Gérard_
%E A015107 Offset changed to 0 by _Seiichi Manyama_, Dec 25 2016