A010983 - OEIS

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

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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