A010983 Binomial coefficient C(n,30).

1, 31, 496, 5456, 46376, 324632, 1947792, 10295472, 48903492, 211915132, 847660528, 3159461968, 11058116888, 36576848168, 114955808528, 344867425584, 991493848554, 2741188875414, 7309837001104, 18851684897584, 47129212243960, 114456658306760, 270533919634160

Offset

30,2

Comments

Coordination sequence for 30-dimensional cyclotomic lattice Z[zeta_31].

Links

T. D. Noe, Table of n, a(n) for n = 30..1000

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

Cf. A001787, A242091.

Sequence in context: A161977 A162378 A162737 * A022595 A125488 A319427

Adjacent sequences: A010980 A010981 A010982 * A010984 A010985 A010986

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved