A010981 - OEIS

A010981

Binomial coefficient C(n,28).

1, 29, 435, 4495, 35960, 237336, 1344904, 6724520, 30260340, 124403620, 472733756, 1676056044, 5586853480, 17620076360, 52860229080, 151532656696, 416714805914, 1103068603890, 2818953098830, 6973199770790, 16735679449896, 39049918716424, 88749815264600

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OFFSET

28,2

COMMENTS

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

LINKS

T. D. Noe, Table of n, a(n) for n = 28..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 (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).

FORMULA

G.f.: x^28/(1-x)^29. - Zerinvary Lajos, Aug 18 2008; adapted to offset by Enxhell Luzhnica, Jan 21 2017

From Amiram Eldar, Dec 12 2020: (Start)

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

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

MAPLE

seq(binomial(n, 28), n=28..53); # Zerinvary Lajos, Aug 18 2008

MATHEMATICA

Table[Binomial[n, 28], {n, 28, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

PROG

(Magma) [Binomial(n, 28): n in [28..60]]; // Vincenzo Librandi, Jun 12 2013

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