The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A004310 Binomial coefficient C(2n,n-4). 3
 1, 10, 66, 364, 1820, 8568, 38760, 170544, 735471, 3124550, 13123110, 54627300, 225792840, 927983760, 3796297200, 15471286560, 62852101650, 254661927156, 1029530696964, 4154246671960, 16735679449896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 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=4. - Herbert Kociemba, May 23 2004 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], p 828 Milan Janjic, Two Enumerative Functions M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - From N. J. A. Sloane, Feb 13 2013 M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5 Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018. FORMULA -(n-4)*(n+4)*a(n) +2*n*(2*n-1)*a(n-1)=0. - R. J. Mathar, Dec 22 2013 G.f.: x*(1/(sqrt(1-4*x)*x)-(1-sqrt(1-4*x))/(2*x^2))/((1-sqrt(1-4*x))/(2*x)-1)^5-(1/x^4-6/x^3+10/x^2-4/x). - Vladimir Kruchinin, Aug 11 2015 a(n) = Sum_{k=0..n} C(n, k)*C(n, k+4). - Hermann Stamm-Wilbrandt, Aug 17 2015 E.g.f.: BesselI(4,2*x)*exp(2*x). - Ilya Gutkovskiy, Jun 27 2019 PROG (MAGMA) [ Binomial(2*n, n-4): n in [4..150] ]; // Vincenzo Librandi, Apr 13 2011 (PARI) first(m)=vector(m, i, binomial(2*(i+3), i-1)) \\ Anders HellstrÃ¶m, Aug 17 2015 CROSSREFS Diagonal 9 of triangle A100257. Sequence in context: A074362 A080421 A320817 * A026853 A177452 A033504 Adjacent sequences:  A004307 A004308 A004309 * A004311 A004312 A004313 KEYWORD nonn,easy AUTHOR 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.

Last modified April 13 09:12 EDT 2021. Contains 342935 sequences. (Running on oeis4.)