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

34,2

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).

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)

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 *)

Prog

(Magma) [Binomial(n, 34): n in [34..70]]; // Vincenzo Librandi, Jun 12 2013
(PARI) x='x+O('x^50); Vec(x^34/(1-x)^35) \\ G. C. Greubel, Nov 23 2017

Crossrefs

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

Sequence in context: A162149 A162384 A126925 * A178353 A202127 A175774

Adjacent sequences: A010984 A010985 A010986 * A010988 A010989 A010990

Keyword

nonn

Author

N. J. A. Sloane

Status

approved