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

40,2

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).

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)

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 *)

Prog

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

Crossrefs

Cf. A001787, A242091.

Sequence in context: A161662 A162178 A162403 * A208431 A275355 A289854

Adjacent sequences: A010990 A010991 A010992 * A010994 A010995 A010996

Keyword

nonn

Author

N. J. A. Sloane

Status

approved