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A185404
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a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+3)*(7k+4).
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3
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1, 168, 97020, 76969200, 70715452500, 70710926711040, 74713950839848320, 82063363963278297600, 92763657280052631873000, 107208829261440251585240000, 126104599836427618807641720480
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OFFSET
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0,2
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LINKS
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FORMULA
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A185403(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+3)*(14k+4).
a(n) ~ cos(Pi/14) * 2^(2*n) * 7^(3*n) / (Pi*n)^(3/2). - Vaclav Kotesovec, Oct 23 2020
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EXAMPLE
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G.f.: A(x) = 1 + 168*x + 97020*x^2 + 76969200*x^3 +...
A(x)^(1/2) = 1 + 84*x + 44982*x^2 + 34706112*x^3 +...+ A185403(n)*x^n +...
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MATHEMATICA
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Table[Binomial[2*n, n]*(7^n/(n!)^2)*Product[(7*k + 3)*(7*k + 4), {k, 0, n - 1}], {n, 0, 50}] (* G. C. Greubel, Jun 29 2017 *)
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PROG
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(PARI) {a(n)=(2*n)!/n!^2*(7^n/n!^2)*prod(k=0, n-1, (7*k+3)*(7*k+4))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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