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A184888 a(n) = C(2n,n) * (8^n/n!^2) * Product_{k=0..n-1} (8k+3)*(8k+5). 1

%I

%S 1,240,205920,243443200,333578044800,497645070354432,

%T 784620394258821120,1286100339771928412160,2169691463830861104076800,

%U 3742512413364745240724275200,6570354792903146744615537541120

%N a(n) = C(2n,n) * (8^n/n!^2) * Product_{k=0..n-1} (8k+3)*(8k+5).

%F Self-convolution of A184887, where

%F A184887(n) = (8^n/n!^2) * Product_{k=0..n-1} (16k+3)*(16k+5).

%F a(n) ~ sqrt(sqrt(2)+2) * 2^(11*n - 1) / (Pi^(3/2) * n^(3/2)). - _Vaclav Kotesovec_, Oct 05 2020

%e G.f.: A(x) = 1 + 240*x + 205920*x^2 + 243443200*x^3 +...

%e A(x)^(1/2) = 1 + 120*x + 95760*x^2 + 110230400*x^3 +...+ A184887(n)*x^n +...

%o (PARI) {a(n)=(2*n)!/n!^2*(8^n/n!^2)*prod(k=0,n-1,(8*k+3)*(8*k+5))}

%Y Cf. A184887, A184898.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 25 2011

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Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)