login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A008979 a(n) = (6n)!/(n!)^6. 7
1, 720, 7484400, 137225088000, 3246670537110000, 88832646059788350720, 2670177736637149247308800, 85722533226982363751829504000, 2889253496242619386328267523990000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

FORMULA

From Peter Bala, Jul 12 2016: (Start)

a(n) = binomial(2*n,n)*binomial(3*n,n)*binomial(4*n,n)*

  binomial(5*n,n)*binomial(6*n,n) = ( [x^n](1 + x)^(2*n) ) * ( [x^n](1 + x)^(3*n) ) * ( [x^n](1 + x)^(4*n) ) * ( [x^n](1 + x)^(5*n) ) * ( [x^n](1 + x)^(6*n) ) = [x^n](F(x)^(720*n)), where F(x) = 1 + x + 4478*x^2 + 53085611*x^3 + 926072057094*x^4 + 19977558181209910*x^5 + 493286693783478576177*x^6 + ... appears to have integer coefficients. For similar results see A000897, A002894, A002897, A006480, A008977, A008978, A186420 and A188662. (End)

a(n) ~ 3^(6*n+1/2)*4^(3*n-1)/(Pi*n)^(5/2). - Ilya Gutkovskiy, Jul 12 2016

MATHEMATICA

Table[(6 n)!/(n)!^6, {n, 0, 20}] (* Vincenzo Librandi, Aug 13 2014 *)

PROG

(MAGMA) [Factorial(6*n)/Factorial(n)^6: n in [0..20]]; // Vincenzo Librandi, Aug 13 2014

CROSSREFS

Cf. A000897, A002894, A002897, A006480, A008977, A008978, A186420, A188662.

Sequence in context: A010799 A075754 A143476 * A158044 A181751 A151596

Adjacent sequences:  A008976 A008977 A008978 * A008980 A008981 A008982

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 17:16 EST 2016. Contains 278890 sequences.