A017733 Binomial coefficients C(n,69).

1, 70, 2485, 59640, 1088430, 16108764, 201359550, 2186189400, 21042072975, 182364632450, 1440680596355, 10477677064400, 70724320184700, 446107250395800, 2644778698775100, 14810760713140560

Offset: 69

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 69..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,69): n in [69..90]]; // G. C. Greubel, Nov 09 2018

Mathematica

Array[Binomial[#, 69] &, 16, 69] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=69, 90, print1(binomial(n,69), ", ")) \\ G. C. Greubel, Nov 09 2018

Sage

[binomial(n, 69) for n in range(69,85)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 09 2018: (Start)

G.f.: x^69/(1-x)^70.

E.g.f.: x^69*exp(x)/69!. (End)

From Amiram Eldar, Dec 17 2020: (Start)

Sum_{n>=69} 1/a(n) = 69/68.

Sum_{n>=69} (-1)^(n+1)/a(n) = A001787(69)*log(2) - A242091(69)/68! = 20365205457375344984064*log(2) - 101282756183642840772927905735657675101997943151 / 7174989242290678616237430 = 0.9861007941... (End)