A010993 Binomial coefficient C(n,40).

1, 41, 861, 12341, 135751, 1221759, 9366819, 62891499, 377348994, 2054455634, 10272278170, 47626016970, 206379406870, 841392966470, 3245372870670, 11899700525790, 41648951840265, 139646485582065, 449972009097765, 1397281501935165, 4191844505805495

Offset: 40

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Coordination sequence for 40-dimensional cyclotomic lattice Z[zeta_41].

Links

• T. D. Noe, Table of n, a(n) for n = 40..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 (41, -820, 10660, -101270, 749398, -4496388, 22481940, -95548245, 350343565, -1121099408, 3159461968, -7898654920, 17620076360, -35240152720, 63432274896, -103077446706, 151584480450, -202112640600, 244662670200, -269128937220, 269128937220, -244662670200, 202112640600, -151584480450, 103077446706, -63432274896, 35240152720, -17620076360, 7898654920, -3159461968, 1121099408, -350343565, 95548245, -22481940, 4496388, -749398, 101270, -10660, 820, -41, 1).

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n, 40): n in [40..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,40),n=40..57); # Zerinvary Lajos, Dec 20 2008

Mathematica

Table[Binomial[n, 40], {n, 5!}] (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *)

Formula

G.f.: x^40/(1-x)^41. - Zerinvary Lajos, Dec 20 2008; adapted to offset by Enxhell Luzhnica, Jan 23 2017

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=40} 1/a(n) = 40/39.

Sum_{n>=40} (-1)^n/a(n) = A001787(40)*log(2) - A242091(40)/39! = 21990232555520*log(2) - 508996625841915892359554528/33393321606645 = 0.9766968066... (End)