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 A324566 a(n) = Product_{i=0..n, j=0..n} (binomial(2*i, i) + binomial(2*j, j)). 3

%I

%S 2,72,2709504,15637972132823040,2676716427588188879089135779840000,

%T 2844659827809077182003221596452154340416256794895644098560000

%N a(n) = Product_{i=0..n, j=0..n} (binomial(2*i, i) + binomial(2*j, j)).

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

%F d = 1.7552437670085151253596298317411616254914764275962173772854884197280838467...

%F alfa = 0.0720289309157636194865104906223497131817905230497828189113545663815669...

%F c = 1.3392511999007422713775779654793976642559410116533455108049762435308676715...

%t Table[Product[Binomial[2*i, i] + Binomial[2*j, j], {i, 0, n}, {j, 0, n}], {n, 0, 7}]

%Y Cf. A000984, A007685, A324565, A324567.

%K nonn

%O 0,1

%A _Vaclav Kotesovec_, Mar 07 2019

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Last modified August 3 17:21 EDT 2021. Contains 346439 sequences. (Running on oeis4.)