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A015096 Carlitz-Riordan q-Catalan numbers (recurrence version) for q=11.

%I A015096 #37 Oct 24 2018 08:22:21
%S A015096 1,1,12,1475,1966284,28792327202,4637090716230072,
%T A015096 8214898341126993790759,160085145151052208703206236460,
%U A015096 34315672899472590258644379240786601502
%N A015096 Carlitz-Riordan q-Catalan numbers (recurrence version) for q=11.
%H A015096 Seiichi Manyama, <a href="/A015096/b015096.txt">Table of n, a(n) for n = 0..44</a>
%H A015096 Robin Sulzgruber, <a href="http://othes.univie.ac.at/30616/">The Symmetry of the q,t-Catalan Numbers</a>, Masterarbeit, University of Vienna. Fakultät für Mathematik, 2013.
%F A015096 a(n+1) = Sum_{i=0..n} q^i*a(i)*a(n-i) with q=11 and a(0)=1.
%F A015096 G.f. satisfies: A(x) = 1 / (1 - x*A(11*x)) = 1/(1-x/(1-11*x/(1-11^2*x/(1-11^3*x/(1-...))))) (continued fraction). - _Seiichi Manyama_, Dec 27 2016
%e A015096 G.f. = 1 + x + 12*x^2 + 1475*x^3 + 1966284*x^4 + 28792327202*x^5 + ...
%t A015096 a[n_] := a[n] = Sum[11^i*a[i]*a[n -i -1], {i, 0, n -1}]; a[0] = 1; Array[a, 16, 0] (* _Robert G. Wilson v_, Dec 24 2016 *)
%o A015096 (Ruby)
%o A015096 def A(q, n)
%o A015096   ary = [1]
%o A015096   (1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + q ** j * ary[j] * ary[i - 1 - j]}}
%o A015096   ary
%o A015096 end
%o A015096 def A015096(n)
%o A015096   A(11, n)
%o A015096 end # _Seiichi Manyama_, Dec 24 2016
%Y A015096 Cf. A227543.
%Y A015096 Cf. A015108 (q=-11), A015107 (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), this sequence (q=11).
%Y A015096 Column k=11 of A090182, A290759.
%K A015096 nonn
%O A015096 0,3
%A A015096 _Olivier Gérard_
%E A015096 Offset changed to 0 by _Seiichi Manyama_, Dec 24 2016