A010992 Binomial coefficient C(n,39).

1, 40, 820, 11480, 123410, 1086008, 8145060, 53524680, 314457495, 1677106640, 8217822536, 37353738800, 158753389900, 635013559600, 2403979904200, 8654327655120, 29749251314475, 97997533741800, 310325523515700, 947309492837400, 2794563003870330

Offset: 39

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 39..1000
• Index entries for linear recurrences with constant coefficients, signature (40, -780, 9880, -91390, 658008, -3838380, 18643560, -76904685, 273438880, -847660528, 2311801440, -5586853480, 12033222880, -23206929840, 40225345056, -62852101650, 88732378800, -113380261800, 131282408400, -137846528820, 131282408400, -113380261800, 88732378800, -62852101650, 40225345056, -23206929840, 12033222880, -5586853480, 2311801440, -847660528, 273438880, -76904685, 18643560, -3838380, 658008, -91390, 9880, -780, 40, -1).

Crossrefs

Cf. A010990, A010991, A001787, A242091.

Programs

Magma

[Binomial(n, 39): n in [39..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,39),n=39..57); # Zerinvary Lajos, Dec 19 2008

Mathematica

Table[Binomial[n,39],{n,39,70}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

Formula

G.f.: x^39/(1-x)^40. - Zerinvary Lajos, Dec 19 2008

From Amiram Eldar, Dec 15 2020: (Start)

Sum_{n>=39} 1/a(n) = 39/38.

Sum_{n>=39} (-1)^(n+1)/a(n) = A001787(39)*log(2) - A242091(39)/38! = 10720238370816*log(2) - 63624578230235205349866541/8562390155550 = 0.9761396932... (End)