A184887 a(n) = (8^n/n!^2) * Product_{k=0..n-1} (16k+3)*(16k+5).
1, 120, 95760, 110230400, 148976385600, 220389705801216, 345522083206128640, 564061275098462085120, 948680557056225919411200, 1632480132897839426558156800, 2860496988068910156792264671232
Offset: 0
Keywords
Examples
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 +...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..100
Programs
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Mathematica
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 *) -
PARI
{a(n)=(8^n/n!^2)*prod(k=0,n-1,(16*k+3)*(16*k+5))}