cp's OEIS Frontend

A130579 Convolution of A000108 (Catalan numbers) and A001764 (ternary trees): a(n) = Sum_{k=0..n} C(2k,k) * C(3(n-k),n-k) / [(k+1)(2(n-k)+1)].

%I A130579 #7 Nov 12 2024 12:07:01
%S A130579 1,2,6,22,92,423,2087,10856,58765,327877,1872490,10890483,64267612,
%T A130579 383773529,2314271146,14071475748,86165249745,530862665988,
%U A130579 3288219482754,20464419717069,127901478759153,802421158028657
%N A130579 Convolution of A000108 (Catalan numbers) and A001764 (ternary trees): a(n) = Sum_{k=0..n} C(2k,k) * C(3(n-k),n-k) / [(k+1)(2(n-k)+1)].
%H A130579 Robert Israel, <a href="/A130579/b130579.txt">Table of n, a(n) for n = 0..1000</a>
%F A130579 G.f.: A(x) = C(x)*T(x) where C(x) = 1 + x*C(x)^2 is the g.f. of A000108 and T(x) = 1 + x*T(x)^3 is the g.f. of A001764.
%F A130579 a(n) ~ 3^(3*n+2) / ((3^(3/2) + sqrt(11)) * sqrt(Pi) * n^(3/2) * 2^(2*n+1)). - _Vaclav Kotesovec_, Nov 12 2024
%p A130579 f:= proc(n) local k; add(binomial(2*k, k)/(k+1)*binomial(3*(n-k), n-k)/(2*(n-k)+1),k=0..n) end proc:
%p A130579 map(f, [$0..25]); # _Robert Israel_, Nov 12 2024
%o A130579 (PARI) a(n)=sum(k=0,n,binomial(2*k,k)/(k+1)*binomial(3*(n-k),n-k)/(2*(n-k)+1))
%Y A130579 Cf. A000108, A001764.
%K A130579 nonn
%O A130579 0,2
%A A130579 _Paul D. Hanna_, Jun 07 2007