A017731 Binomial coefficients C(n,67).

1, 68, 2346, 54740, 971635, 13991544, 170230452, 1799579064, 16871053725, 142466675900, 1096993404430, 7778680504140, 51209646652255, 315136287090800, 1823288518168200, 9967310565986160, 51705423561053205

Offset: 67

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 67..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,67): n in [67..90]]; // G. C. Greubel, Nov 08 2018

Mathematica

Array[Binomial[#, 67] &, 17, 67]

PARI

for(n=67, 90, print1(binomial(n,67), ", ")) \\ G. C. Greubel, Nov 08 2018

Sage

[binomial(n, 67) for n in range(67,84)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 03 2018: (Start)

G.f.: x^67/(1-x)^68.

E.g.f.: x^67*exp(x)/67!. (End)

From Amiram Eldar, Dec 17 2020: (Start)

Sum_{n>=67} 1/a(n) = 67/66.

Sum_{n>=67} (-1)^(n+1)/a(n) = A001787(67)*log(2) - A242091(67)/66! = 4943727411754159833088*log(2) - 202565512367285681545811693791632836799528091007 / 59113344205141113375568080 = 0.9857030700... (End)