A010989 Binomial coefficient C(n,36).

1, 37, 703, 9139, 91390, 749398, 5245786, 32224114, 177232627, 886163135, 4076350421, 17417133617, 69668534468, 262596783764, 937845656300, 3188675231420, 10363194502115, 32308782859535, 96926348578605, 280576272201225, 785613562163430, 2132379668729310

Offset: 36

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Coordination sequence for 36-dimensional cyclotomic lattice Z[zeta_37].

Links

• T. D. Noe, Table of n, a(n) for n = 36..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 (37, -666, 7770, -66045, 435897, -2324784, 10295472, -38608020, 124403620, -348330136, 854992152, -1852482996, 3562467300, -6107086800, 9364199760, -12875774670, 15905368710, -17672631900, 17672631900, -15905368710, 12875774670, -9364199760, 6107086800, -3562467300, 1852482996, -854992152, 348330136, -124403620, 38608020, -10295472, 2324784, -435897, 66045, -7770, 666, -37, 1).

Crossrefs

Cf. A010986, A010987, A010988, A001787, A242091.

Programs

Magma

[Binomial(n, 36): n in [36..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,36),n=36..55); # Zerinvary Lajos, Dec 19 2008

Mathematica

Table[Binomial[n,36],{n,36,66}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

Formula

G.f.: x^36/(1-x)^37. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 23 2017

From Amiram Eldar, Dec 12 2020: (Start)

Sum_{n>=36} 1/a(n) = 36/35.

Sum_{n>=36} (-1)^n/a(n) = A001787(36)*log(2) - A242091(36)/35! = 1236950581248*log(2) - 429895798852508537154517/501401225325 = 0.9742957989... (End)