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A324565 a(n) = Product_{i=0..n, j=0..n} (C(i)+C(j)), where C(k) = Catalan(k) = A000108(k). 1

%I

%S 2,16,5184,3292047360,431257150704844800000,

%T 1660988174371634812975670031600844800000,

%U 29842277901990912803108442836098281105491323166448779304684748800000

%N a(n) = Product_{i=0..n, j=0..n} (C(i)+C(j)), where C(k) = Catalan(k) = A000108(k).

%F a(n) ~ c * d^n * 2^(4*n^3/3 + 3*n^2) * exp(3*n^2/4) / (Pi^(n^2/2) * n^(3*n^2/2 + 3*n - alfa)), where

%F d = 1.755243767008515125359629831741161625491476427596217377285488419728083846...

%F alfa = 0.033913207252709141540468528132950860454628430850651543265936300855299...

%F c = 1.31959917222402005903928675604752142566298009509...

%t Table[Product[CatalanNumber[i] + CatalanNumber[j], {i, 0, n}, {j, 0, n}], {n, 0, 7}]

%Y Cf. A000108, A003046, A324566.

%K nonn

%O 0,1

%A _Vaclav Kotesovec_, Mar 07 2019

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Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)