|
| |
|
|
A071798
|
|
Number of paths on the surface of the n-dimensional lattice [0..2]^n; i.e. the lattice paths that do not pass through the point (1,1,...,1).
|
|
1
| |
|
|
0, 2, 54, 1944, 99000, 6966000, 655678800, 80103945600, 12372954249600, 2362712677920000, 547235129437920000, 151247218046601600000, 49191138900262719360000, 18601307697723249058560000, 8093164859945489259936000000, 4014620173473616480790016000000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| a(2) + 1 = 3 is prime. a(3) - 1 = 53 is prime. a(5) - 1 = 98999 is prime. a(7) + 1 = 655678801 is prime. a(8) - 1 = 80103945599 is prime, and part of a twin prime, as a(8) + 1 = 80103945601 is prime. a(13) - 1 = 49191138900262719359999 is prime. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 01 2009]
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..50
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
|
FORMULA
| a(n)=(2n)!/2^n-(n!)^2
|
|
|
MATHEMATICA
| Table[(2n)!/2^n-(n!)^2, {n, 10}]
|
|
|
CROSSREFS
| Cf. A000680.
Sequence in context: A055024 A057411 A157058 * A123686 A122418 A069788
Adjacent sequences: A071795 A071796 A071797 * A071799 A071800 A071801
|
|
|
KEYWORD
| easy,nice,nonn
|
|
|
AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jun 06 2002
|
|
|
EXTENSIONS
| Situations in which a(n) -1 or a(n)+1 are primes for n = 1..30. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 01 2009]
More terms from Harvey P. Dale, May 26 2011.
|
| |
|
|
