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!)
A199748 a(n) = binomial(n*(3*n-1)/2, n). 2
1, 1, 10, 220, 7315, 324632, 18009460, 1198774720, 93080887185, 8258898672310, 824313388697656, 91408035226209520, 11149106984707682900, 1483408105790477598270, 213807915740948618992925, 33186033477308745271085760, 5518696446064784220490766525 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..300

FORMULA

a(n) = binomial(A000326(n), n), where A000326 are pentagonal numbers.

a(n) is divisible by 5 for gcd(n,5) = 1 and n>0.

a(n) ~ n^(n-1/2) * exp(n-2/3) * 3^n / (sqrt(Pi) * 2^(n+1/2)). - Vaclav Kotesovec, Apr 23 2015

EXAMPLE

a(2) = C(5,2) = 10; a(3) = C(12,3) = 220; a(4) = C(22,4) = 7315; a(5) = C(35,5) = 324632; ...

MATHEMATICA

Table[Binomial[n*(3n-1)/2, n], {n, 0, 20}] (* Harvey P. Dale, Aug 16 2012 *)

PROG

(PARI) {a(n)=binomial(n*(3*n-1)/2, n)}

CROSSREFS

Cf. A199747, A000326, A001318.

Sequence in context: A053131 A334908 A166181 * A210137 A064333 A223817

Adjacent sequences:  A199745 A199746 A199747 * A199749 A199750 A199751

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 09 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 24 22:45 EST 2022. Contains 350565 sequences. (Running on oeis4.)