A010994 a(n) = binomial coefficient C(n,41).

1, 42, 903, 13244, 148995, 1370754, 10737573, 73629072, 450978066, 2505433700, 12777711870, 60403728840, 266783135710, 1108176102180, 4353548972850, 16253249498640, 57902201338905, 197548686920970, 647520696018735, 2044802197953900, 6236646703759395

Offset: 41

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 41..1000
• Index entries for linear recurrences with constant coefficients, signature (42, -861, 11480, -111930, 850668, -5245786, 26978328, -118030185, 445891810, -1471442973, 4280561376, -11058116888, 25518731280, -52860229080, 98672427616, -166509721602, 254661927156, -353697121050, 446775310800, -513791607420, 538257874440, -513791607420, 446775310800, -353697121050, 254661927156, -166509721602, 98672427616, -52860229080, 25518731280, -11058116888, 4280561376, -1471442973, 445891810, -118030185, 26978328, -5245786, 850668, -111930, 11480, -861, 42, -1).

Crossrefs

Cf. A010990, A010991, A010992, A001787, A242091.

Programs

Magma

[Binomial(n, 41): n in [41..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,41),n=41..57); # Zerinvary Lajos, Dec 20 2008

Mathematica

Table[Binomial[n,41],{n,41,70}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

Formula

G.f.: x^41/(1-x)^42. - Zerinvary Lajos, Dec 20 2008

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=41} 1/a(n) = 41/40.

Sum_{n>=41} (-1)^(n+1)/a(n) = A001787(41)*log(2) - A242091(41)/40! = 45079976738816*log(2) - 41737723319038472299669343741/1335732864265800 = 0.9772284535... (End)