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!)
A184891 a(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+1)*(10k+4). 6
1, 20, 3850, 1078000, 355066250, 128107903000, 49001272897500, 19520507080800000, 8012558140822125000, 3365274419145292500000, 1439327869068441602250000, 624739666805574817770000000 (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) = A184892(n) where
. A184892(n) = C(2n,n) * (5^n/n!^2)*Product_{k=0..n-1} (5k+1)*(5k+4).
EXAMPLE
G.f.: A(x) = 1 + 20*x + 3850*x^2 + 1078000*x^3 +...
A(x)^2 = 1 + 40*x + 8100*x^2 + 2310000*x^3 +...+ A184892(n)*x^n +...
MATHEMATICA
Table[5^n/(n!)^2 Product[(10k+1)(10k+4), {k, 0, n-1}], {n, 0, 20}] (* Harvey P. Dale, Feb 02 2012 *)
FullSimplify[Table[2^(2*n) * 5^(3*n) * Gamma[n+1/10] * Gamma[n+2/5] / (Gamma[2/5] * Gamma[1/10] * Gamma[n+1]^2), {n, 0, 15}]] (* Vaclav Kotesovec, Jul 03 2014 *)
PROG
(PARI) {a(n)=(5^n/n!^2)*prod(k=0, n-1, (10*k+1)*(10*k+4))}
CROSSREFS
Sequence in context: A225989 A332265 A177323 * A279297 A079759 A109894
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 July 13 23:31 EDT 2024. Contains 374290 sequences. (Running on oeis4.)