A010998 a(n) = binomial coefficient C(n,45).

1, 46, 1081, 17296, 211876, 2118760, 18009460, 133784560, 886322710, 5317936260, 29248649430, 148902215280, 707285522580, 3155581562280, 13298522298180, 53194089192720, 202802465047245, 739632519584070, 2588713818544245, 8719878125622720, 28339603908273840

Offset: 45

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 45..1000
• Index entries for linear recurrences with constant coefficients, signature (46, -1035, 15180, -163185, 1370754, -9366819, 53524680, -260932815, 1101716330, -4076350421, 13340783196, -38910617655, 101766230790, -239877544005, 511738760544, -991493848554, 1749695026860, -2818953098830, 4154246671960, -5608233007146, 6943526580276, -7890371113950, 8233430727600, -7890371113950, 6943526580276, -5608233007146, 4154246671960, -2818953098830, 1749695026860, -991493848554, 511738760544, -239877544005, 101766230790, -38910617655, 13340783196, -4076350421, 1101716330, -260932815, 53524680, -9366819, 1370754, -163185, 15180, -1035, 46, -1).

Crossrefs

Cf. A010996, A010997, A001787, A242091.

Programs

Magma

[Binomial(n, 45): n in [45..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,45),n=45..67); # Zerinvary Lajos, Dec 20 2008

Mathematica

Table[Binomial[n,45],{n,45,77}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

Formula

G.f.: x^45/(1-x)^46. - Zerinvary Lajos, Dec 20 2008

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=45} 1/a(n) = 45/44.

Sum_{n>=45} (-1)^(n+1)/a(n) = A001787(45)*log(2) - A242091(45)/44! = 791648371998720*log(2) - 14357776821749657880334247281129/26165522663340060 = 0.9791324188... (End)