|
|
A004311
|
|
Binomial coefficient C(2n,n-5).
|
|
4
|
|
|
1, 12, 91, 560, 3060, 15504, 74613, 346104, 1562275, 6906900, 30045015, 129024480, 548354040, 2310789600, 9669554100, 40225345056, 166509721602, 686353797976, 2818953098830, 11541847896480, 47129212243960, 191991813933920, 780512175396135, 3167295784216200
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
5,2
|
|
COMMENTS
|
Number of lattice paths from (0,0) to (n,n) with steps E=(1,0) and N=(0,1) which touch or cross the line x-y=5. - Herbert Kociemba, May 24 2004
|
|
REFERENCES
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
|
|
LINKS
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
|
|
FORMULA
|
-(n-5)*(n+5)*a(n) +2*n*(2*n-1)*a(n-1)=0. - R. J. Mathar, Jan 24 2018
Sum_{n>=5} 1/a(n) = 6169/840 - 31*Pi/(9*sqrt(3)).
Sum_{n>=5} (-1)^(n+1)/a(n) = 5254*log(phi)/(5*sqrt(5)) - 63059/280, where phi is the golden ratio (A001622). (End)
|
|
MATHEMATICA
|
Table[Binomial[2*n, n-5], {n, 5, 30}] (* Amiram Eldar, Aug 27 2022 *)
|
|
PROG
|
(PARI) first(m)=vector(m, i, binomial(2*(i+4), i-1)) \\ Anders Hellström, Aug 17 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|