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A184897
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a(n) = (8^n/n!^2) * Product_{k=0..n-1} (16k+1)*(16k+7).
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6
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1, 56, 43792, 50098048, 67507119680, 99694514343424, 156121609461801984, 254663020429855285248, 428056704465033002591232, 736257531679856764456919040, 1289628692490437108622739390464
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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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Self-convolution yields Sum_{k=0..n} a(n-k)*a(k) = A184898(n) where A184898(n) = C(2n,n) * (8^n/n!^2)*Product_{k=0..n-1} (8k+1)*(8k+7).
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EXAMPLE
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G.f.: A(x) = 1 + 56*x + 43792*x^2 + 50098048*x^3 +...
A(x)^2 = 1 + 112*x + 90720*x^2 + 105100800*x^3 +...+ A184898(n)*x^n +...
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MATHEMATICA
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FullSimplify[Table[2^(11*n) * Gamma[n+1/16] * Gamma[n+7/16] / (Gamma[n+1]^2 * Gamma[1/16] * Gamma[7/16]), {n, 0, 15}]] (* Vaclav Kotesovec, Jul 03 2014 *)
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PROG
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(PARI) {a(n)=(8^n/n!^2)*prod(k=0, n-1, (16*k+1)*(16*k+7))}
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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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