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A239453 Convolution of the generalized Catalan numbers A057977 with themselves.

%I A239453 #11 Feb 03 2025 09:40:47
%S A239453 1,2,3,8,11,30,43,112,172,420,694,1584,2809,6006,11379,22880,46088,
%T A239453 87516,186562,335920,754646,1293292,3050238,4992288,12319816,19315400,
%U A239453 49725004,74884320,200571541,290845350,808559299,1131445440,3257808976,4407922860,13119940234
%N A239453 Convolution of the generalized Catalan numbers A057977 with themselves.
%F A239453 D-finite with recurrence -(n+4)*(137*n-1035)*a(n) +(383*n^2-1622*n-5421)*a(n-1) +4*(274*n^2-1385*n-3534)*a(n-2) +4*(-766*n^2+4393*n+555)*a(n-3) +16*(-137*n^2+898*n-606)*a(n-4) +16*(n-3)*(383*n-1622)*a(n-5)=0. - _R. J. Mathar_, Feb 03 2025
%o A239453 (Sage)
%o A239453 def A239453_list(n):
%o A239453     r = sqrt(1-4*x^2)
%o A239453     g = lambda x: (1-r)*(r+x)/(2*x^2*r)
%o A239453     s = taylor(g(x), x, 0, n+1)
%o A239453     f = [s.coefficient(x, j) for j in (0..n+1)]
%o A239453     return [add(f[k]*f[j-k] for k in (0..j)) for j in (0..n)]
%o A239453 A239453_list(36)
%Y A239453 Cf. A162551.
%K A239453 nonn
%O A239453 0,2
%A A239453 _Peter Luschny_, Mar 19 2014