|
| |
| |
|
|
|
1, 24, 2520, 369600, 63063000, 11732745024, 2308743493056, 472518347558400, 99561092450391000, 21452752266265320000, 4705360871073570227520, 1047071828879079131681280, 235809301462142612780721600
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Number of paths of length 4n in an n X n X n X n grid from (0,0,0,0) to (n,n,n,n).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
R. M. Dickau, Paths through a 4-D lattice
|
|
|
FORMULA
| a(n) = A139541(n)*(A001316(n)/A049606(n))^3. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 28 2008
Self-convolution of A178529, where A178529(n) = (4^n/n!^2) * Product_{k=0..n-1} (8*k+1)*(8*k+3).
G.f.: hypergeom([1/8, 3/8], [1], 256*x)^2 - Mark van Hoeij, Nov 16 2011
|
|
|
EXAMPLE
| a(13)=52!/(13!)^4=53644737765488792839237440000 is the number of ways of dealing the four hands in Bridge or Whist - Henry Bottomley (se16(AT)btinternet.com), Oct 06 2000
|
|
|
MAPLE
| A008977 := n->(4*n)!/(n!)^4;
|
|
|
MATHEMATICA
| Table[(4n)!/(n!)^4, {n, 0, 16}] (* From Harvey P. Dale, Oct 24 2011 *)
|
|
|
CROSSREFS
| Cf. A000984, A006480, A008978, A178529.
Sequence in context: A107675 A173115 A202927 * A159392 A064596 A092706
Adjacent sequences: A008974 A008975 A008976 * A008978 A008979 A008980
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
