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

36,2

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).

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)

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 *)

Prog

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

Crossrefs

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

Sequence in context: A161650 A162165 A162389 * A103195 A282927 A220684

Adjacent sequences: A010986 A010987 A010988 * A010990 A010991 A010992

Keyword

nonn

Author

N. J. A. Sloane

Status

approved