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

%I #11 Jul 04 2014 03:58:29

%S 1,120,95760,110230400,148976385600,220389705801216,

%T 345522083206128640,564061275098462085120,948680557056225919411200,

%U 1632480132897839426558156800,2860496988068910156792264671232

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

%H Vincenzo Librandi, <a href="/A184887/b184887.txt">Table of n, a(n) for n = 0..100</a>

%F 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).

%e G.f.: A(x) = 1 + 120*x + 95760*x^2 + 110230400*x^3 +...

%e A(x)^2 = 1 + 240*x + 205920*x^2 + 243443200*x^3 +...+ A184888(n)*x^n +...

%t 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 *)

%o (PARI) {a(n)=(8^n/n!^2)*prod(k=0,n-1,(16*k+3)*(16*k+5))}

%Y Cf. A184888, A184897.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 25 2011

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