A010995 Binomial coefficient C(n,42).

1, 43, 946, 14190, 163185, 1533939, 12271512, 85900584, 536878650, 3042312350, 15820024220, 76223753060, 343006888770, 1451182990950, 5804731963800, 22057981462440, 79960182801345, 277508869722315, 925029565741050, 2969831763694950, 9206478467454345

Offset: 42

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Coordination sequence for 42-dimensional cyclotomic lattice Z[zeta_43].

Links

• T. D. Noe, Table of n, a(n) for n = 42..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 (43, -903, 12341, -123410, 962598, -6096454, 32224114, -145008513, 563921995, -1917334783, 5752004349, -15338678264, 36576848168, -78378960360, 151532656696, -265182149218, 421171648758, -608359048206, 800472431850, -960566918220, 1052049481860, -1052049481860, 960566918220, -800472431850, 608359048206, -421171648758, 265182149218, -151532656696, 78378960360, -36576848168, 15338678264, -5752004349, 1917334783, -563921995, 145008513, -32224114, 6096454, -962598, 123410, -12341, 903, -43, 1).

Crossrefs

Cf. A010992, A010994, A001787, A242091.

Programs

Magma

[Binomial(n, 42): n in [42..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,42),n=42..57); # Zerinvary Lajos, Dec 20 2008

Mathematica

Table[Binomial[n,42],{n,42,70}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

Formula

G.f.: x^42/(1-x)^43. - Zerinvary Lajos, Dec 20 2008

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=42} 1/a(n) = 42/41.

Sum_{n>=42} (-1)^n/a(n) = A001787(42)*log(2) - A242091(42)/41! = 92358976733184*log(2) - 41737723319039140166101476641/651964850415450 = 0.9777363438... (End)