A010999 a(n) = binomial coefficient C(n,46).

1, 47, 1128, 18424, 230300, 2349060, 20358520, 154143080, 1040465790, 6358402050, 35607051480, 184509266760, 891794789340, 4047376351620, 17345898649800, 70539987842520, 273342452889765, 1012974972473835, 3601688791018080, 12321566916640800, 40661170824914640

Offset: 46

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Coordination sequence for 46-dimensional cyclotomic lattice Z[zeta_47].

Links

• T. D. Noe, Table of n, a(n) for n = 46..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 (47, -1081, 16215, -178365, 1533939, -10737573, 62891499, -314457495, 1362649145, -5178066751, 17417133617, -52251400851, 140676848445, -341643774795, 751616304549, -1503232609098, 2741188875414, -4568648125690, 6973199770790, -9762479679106, 12551759587422, -14833897694226, 16123801841550, -16123801841550, 14833897694226, -12551759587422, 9762479679106, -6973199770790, 4568648125690, -2741188875414, 1503232609098, -751616304549, 341643774795, -140676848445, 52251400851, -17417133617, 5178066751, -1362649145, 314457495, -62891499, 10737573, -1533939, 178365, -16215, 1081, -47, 1).

Crossrefs

Cf. A010997, A010998, A001787, A242091.

Programs

Magma

[Binomial(n, 46): n in [46..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,46),n=46..67); # Zerinvary Lajos, Dec 20 2008

Mathematica

Table[Binomial[n,46],{n,46,77}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

Formula

G.f.: x^46/(1-x)^47. - Zerinvary Lajos, Dec 20 2008

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=46} 1/a(n) = 46/45.

Sum_{n>=46} (-1)^n/a(n) = A001787(46)*log(2) - A242091(46)/45! = 1618481116086272*log(2) - 14357776821749670963095578951159/12798353476633725 = 0.9795596119... (End)