A017748 Binomial coefficients C(n,84).

1, 85, 3655, 105995, 2331890, 41507642, 622614630, 8093990190, 93080887185, 961835834245, 9041256841903, 78083581816435, 624668654531480, 4660989191504120, 32626924340528840, 215337700647490344

Offset: 84

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 84..10000

Crossrefs

Cf. A001787, A242091.

Programs

GAP

List([84..100], n->Binomial(n,84)); # Muniru A Asiru, Nov 11 2018

Magma

[Binomial(n,84): n in [84..105]]; // G. C. Greubel, Nov 10 2018

Maple

seq(binomial(n,84),n=84..100); # Muniru A Asiru, Nov 11 2018

Mathematica

Array[Binomial[#, 84] &, 16, 84] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=84, 105, print1(binomial(n,84), ", ")) \\ G. C. Greubel, Nov 10 2018

Sage

[binomial(n, 84) for n in range(84,100)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 10 2018: (Start)

G.f.: x^84/(1-x)^85.

E.g.f.: x^84*exp(x)/84!. (End)

From Amiram Eldar, Dec 18 2020: (Start)

Sum_{n>=84} 1/a(n) = 84/83.

Sum_{n>=84} (-1)^n/a(n) = A001787(84)*log(2) - A242091(84)/83! = 812398150781030805402550272*log(2) - 3383709676723495179693767384107675907832497859728358144156958 / 6008951603008706655501540404837775 = 0.9884998637... (End)