The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A010983 Binomial coefficient C(n,30). 3
1, 31, 496, 5456, 46376, 324632, 1947792, 10295472, 48903492, 211915132, 847660528, 3159461968, 11058116888, 36576848168, 114955808528, 344867425584, 991493848554, 2741188875414, 7309837001104, 18851684897584, 47129212243960, 114456658306760, 270533919634160 (list; graph; refs; listen; history; text; internal format)
OFFSET
30,2
COMMENTS
Coordination sequence for 30-dimensional cyclotomic lattice Z[zeta_31].
LINKS
Matthias Beck and Serkan Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.
Index entries for linear recurrences with constant coefficients, signature (31, -465, 4495, -31465, 169911, -736281, 2629575, -7888725, 20160075, -44352165, 84672315, -141120525, 206253075, -265182525, 300540195, -300540195, 265182525, -206253075, 141120525, -84672315, 44352165, -20160075, 7888725, -2629575, 736281, -169911, 31465, -4495, 465, -31, 1).
FORMULA
G.f.: x^30/(1-x)^31. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 21 2017
From Amiram Eldar, Dec 12 2020: (Start)
Sum_{n>=30} 1/a(n) = 30/29.
Sum_{n>=30} (-1)^n/a(n) = A001787(30)*log(2) - A242091(30)/29! = 16106127360*log(2) - 108340675104753102419/9704539845 = 0.9695936954... (End)
MAPLE
seq(binomial(n, 30), n=30..53); # Zerinvary Lajos, Dec 19 2008
MATHEMATICA
Table[Binomial[n, 30], {n, 5!}] (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *)
PROG
(Magma) [Binomial(n, 30): n in [30..70]]; // Vincenzo Librandi, Jun 12 2013
(PARI) x='x+O('x^50); Vec(x^30/(1-x)^31) \\ G. C. Greubel, Nov 23 2017
CROSSREFS
Sequence in context: A161977 A162378 A162737 * A022595 A125488 A319427
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 09:23 EDT 2024. Contains 372786 sequences. (Running on oeis4.)