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Binomial coefficient C(n,30).
3

%I #43 Dec 15 2023 10:42:01

%S 1,31,496,5456,46376,324632,1947792,10295472,48903492,211915132,

%T 847660528,3159461968,11058116888,36576848168,114955808528,

%U 344867425584,991493848554,2741188875414,7309837001104,18851684897584,47129212243960,114456658306760,270533919634160

%N Binomial coefficient C(n,30).

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

%H T. D. Noe, <a href="/A010983/b010983.txt">Table of n, a(n) for n = 30..1000</a>

%H Matthias Beck and Serkan Hosten, <a href="http://arxiv.org/abs/math/0508136">Cyclotomic polytopes and growth series of cyclotomic lattices</a>, arXiv:math/0508136 [math.CO], 2005-2006.

%H <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, 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).

%F G.f.: x^30/(1-x)^31. - _Zerinvary Lajos_, Dec 19 2008; adapted to offset by _Enxhell Luzhnica_, Jan 21 2017

%F From _Amiram Eldar_, Dec 12 2020: (Start)

%F Sum_{n>=30} 1/a(n) = 30/29.

%F Sum_{n>=30} (-1)^n/a(n) = A001787(30)*log(2) - A242091(30)/29! = 16106127360*log(2) - 108340675104753102419/9704539845 = 0.9695936954... (End)

%p seq(binomial(n,30),n=30..53);# _Zerinvary Lajos_, Dec 19 2008

%t Table[Binomial[n, 30], {n, 5!}] (* _Vladimir Joseph Stephan Orlovsky_, Sep 25 2008 *)

%o (Magma) [Binomial(n, 30): n in [30..70]]; // _Vincenzo Librandi_, Jun 12 2013

%o (PARI) x='x+O('x^50); Vec(x^30/(1-x)^31) \\ _G. C. Greubel_, Nov 23 2017

%Y Cf. A001787, A242091.

%K nonn,easy

%O 30,2

%A _N. J. A. Sloane_