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

42,2

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).

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)

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 *)

Prog

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

Crossrefs

Cf. A010992, A010994, A001787, A242091.

Sequence in context: A161668 A162181 A162412 * A253915 A288031 A265658

Adjacent sequences: A010992 A010993 A010994 * A010996 A010997 A010998

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved