A010987 Binomial coefficient C(n,34).

1, 35, 630, 7770, 73815, 575757, 3838380, 22481940, 118030185, 563921995, 2481256778, 10150595910, 38910617655, 140676848445, 482320623240, 1575580702584, 4923689695575, 14771069086725, 42671977361650, 119032357903550, 321387366339585, 841728816603675

Offset: 34

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 34..1000
• Index entries for linear recurrences with constant coefficients, signature (35, -595, 6545, -52360, 324632, -1623160, 6724520, -23535820, 70607460, -183579396, 417225900, -834451800, 1476337800, -2319959400, 3247943160, -4059928950, 4537567650, -4537567650, 4059928950, -3247943160, 2319959400, -1476337800, 834451800, -417225900, 183579396, -70607460, 23535820, -6724520, 1623160, -324632, 52360, -6545, 595, -35, 1).

Crossrefs

Cf. A010984, A010985, A010986, A001787, A242091.

Programs

Magma

[Binomial(n, 34): n in [34..70]]; // Vincenzo Librandi, Jun 12 2013

Maple

seq(binomial(n,34),n=34..55); # Zerinvary Lajos, Dec 19 2008

Mathematica

Table[Binomial[n,34],{n,34,60}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

PARI

x='x+O('x^50); Vec(x^34/(1-x)^35) \\ G. C. Greubel, Nov 23 2017

Formula

G.f.: x^34/(1-x)^35 . - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 23 2017

From Amiram Eldar, Dec 12 2020: (Start)

Sum_{n>=34} 1/a(n) = 34/33.

Sum_{n>=34} (-1)^n/a(n) = A001787(34)*log(2) - A242091(34)/33! = 292057776128*log(2) - 429895798850931019349797/2123581660200 = 0.9728992064... (End)