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A184887
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a(n) = (8^n/n!^2) * Product_{k=0..n-1} (16k+3)*(16k+5).
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2
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1, 120, 95760, 110230400, 148976385600, 220389705801216, 345522083206128640, 564061275098462085120, 948680557056225919411200, 1632480132897839426558156800, 2860496988068910156792264671232
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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) = A184888(n) where: A184888(n) = C(2n,n) * (8^n/n!^2)*Product_{k=0..n-1} (8k+3)*(8k+5).
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EXAMPLE
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G.f.: A(x) = 1 + 120*x + 95760*x^2 + 110230400*x^3 +...
A(x)^2 = 1 + 240*x + 205920*x^2 + 243443200*x^3 +...+ A184888(n)*x^n +...
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MATHEMATICA
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FullSimplify[Table[2^(11*n) * Gamma[n+3/16] * Gamma[n+5/16] / (Gamma[n+1]^2 * Gamma[3/16] * Gamma[5/16]), {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+3)*(16*k+5))}
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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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