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Binomial coefficient C(n,28).
5

%I #44 Dec 15 2023 15:39:55

%S 1,29,435,4495,35960,237336,1344904,6724520,30260340,124403620,

%T 472733756,1676056044,5586853480,17620076360,52860229080,151532656696,

%U 416714805914,1103068603890,2818953098830,6973199770790,16735679449896,39049918716424,88749815264600

%N Binomial coefficient C(n,28).

%C Coordination sequence for 28-dimensional cyclotomic lattice Z[zeta_29].

%H T. D. Noe, <a href="/A010981/b010981.txt">Table of n, a(n) for n = 28..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_29">Index entries for linear recurrences with constant coefficients</a>, signature (29, -406, 3654, -23751, 118755, -475020, 1560780, -4292145, 10015005, -20030010, 34597290, -51895935, 67863915, -77558760, 77558760, -67863915, 51895935, -34597290, 20030010, -10015005, 4292145, -1560780, 475020, -118755, 23751, -3654, 406, -29, 1).

%F G.f.: x^28/(1-x)^29. - _Zerinvary Lajos_, Aug 18 2008; adapted to offset by _Enxhell Luzhnica_, Jan 21 2017

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

%F Sum_{n>=28} 1/a(n) = 28/27.

%F Sum_{n>=28} (-1)^n/a(n) = A001787(28)*log(2) - A242091(28)/27! = 3758096384*log(2) - 1867942673688249668/717084225 = 0.9676178392... (End)

%p seq(binomial(n,28),n=28..53); # _Zerinvary Lajos_, Aug 18 2008

%t Table[Binomial[n,28],{n,28,60}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 26 2011 *)

%o (Magma) [Binomial(n, 28): n in [28..60]]; // _Vincenzo Librandi_, Jun 12 2013

%o (PARI) x='x+O('x^50); Vec(x^28/(1-x)^29) \\ _G. C. Greubel_, Nov 23 2017

%Y Cf. A010980, A001787, A242091.

%K nonn,easy

%O 28,2

%A _N. J. A. Sloane_