A010996 Binomial coefficient C(n,43).

1, 44, 990, 15180, 178365, 1712304, 13983816, 99884400, 636763050, 3679075400, 19499099620, 95722852680, 438729741450, 1889912732400, 7694644696200, 29752626158640, 109712808959985, 387221678682300, 1312251244423350, 4282083008118300, 13488561475572645

Offset: 43

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 43..1000
• Index entries for linear recurrences with constant coefficients, signature (44, -946, 13244, -135751, 1086008, -7059052, 38320568, -177232627, 708930508, -2481256778, 7669339132, -21090682613, 51915526432, -114955808528, 229911617056, -416714805914, 686353797976, -1029530696964, 1408831480056, -1761039350070, 2012616400080, -2104098963720, 2012616400080, -1761039350070, 1408831480056, -1029530696964, 686353797976, -416714805914, 229911617056, -114955808528, 51915526432, -21090682613, 7669339132, -2481256778, 708930508, -177232627, 38320568, -7059052, 1086008, -135751, 13244, -946, 44, -1).

Crossrefs

Cf. A010994, A010996, A001787, A242091.

Programs

Magma

[Binomial(n, 43): n in [43..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,43),n=43..57); # Zerinvary Lajos, Dec 20 2008

Mathematica

Table[Binomial[n, 43], {n, 43, 70}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

Formula

G.f.: x^43/(1-x)^44. - Zerinvary Lajos, Dec 20 2008

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=43} 1/a(n) = 43/42.

Sum_{n>=43} (-1)^(n+1)/a(n) = A001787(43)*log(2) - A242091(43)/42! = 189115999977472*log(2) - 897361051359348522193323713869/6845630929362225 = 0.9782220374... (End)