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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A004314 a(n) = binomial coefficient C(2n, n - 8). 1
1, 18, 190, 1540, 10626, 65780, 376740, 2035800, 10518300, 52451256, 254186856, 1203322288, 5586853480, 25518731280, 114955808528, 511738760544, 2254848913647, 9847379391150, 42671977361650 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

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

Table of n, a(n) for n=8..26.

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].

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.

FORMULA

-(n - 8)*(n + 8)*a(n) + 2*n*(2*n - 1)*a(n - 1) = 0. - R. J. Mathar, Dec 10 2013

E.g.f.: BesselI(8,2*x)*exp(2*x). - Ilya Gutkovskiy, Jun 27 2019

MATHEMATICA

a[n_]:=Binomial[2*n, n - 8]; Array[a, 150, 8] (* Stefano Spezia, Sep 01 2018 *)

PROG

(MAGMA) [Binomial(2*n, n - 8): n in [8..150] ]; // Vincenzo Librandi, Apr 13 2011

CROSSREFS

Sequence in context: A022646 A268447 A259163 * A125406 A318161 A182311

Adjacent sequences:  A004311 A004312 A004313 * A004315 A004316 A004317

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 20 10:09 EST 2019. Contains 329334 sequences. (Running on oeis4.)