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.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
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
1, 120, 95760, 110230400, 148976385600, 220389705801216, 345522083206128640, 564061275098462085120, 948680557056225919411200, 1632480132897839426558156800, 2860496988068910156792264671232 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
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).
EXAMPLE
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 +...
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 *)
PROG
(PARI) {a(n)=(8^n/n!^2)*prod(k=0, n-1, (16*k+3)*(16*k+5))}
CROSSREFS
Sequence in context: A058528 A001421 A107446 * A279579 A159735 A157879
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 25 2011
STATUS
approved

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 21 14:18 EDT 2024. Contains 372738 sequences. (Running on oeis4.)