The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 15 22:50 EDT 2024. Contains 373412 sequences. (Running on oeis4.)