A017747 Binomial coefficients C(n,83).

1, 84, 3570, 102340, 2225895, 39175752, 581106988, 7471375560, 84986896995, 868754947060, 8079421007658, 69042324974532, 546585072715045, 4036320536972640, 27965935149024720, 182710776306961504

Offset: 83

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 83..10000

Crossrefs

Cf. A001787, A242091.

Programs

GAP

List([83..100], n->Binomial(n,83)); # Muniru A Asiru, Nov 11 2018

Magma

[Binomial(n,83): n in [83..100]]; // G. C. Greubel, Nov 10 2018

Maple

seq(binomial(n,83),n=83..100); # Muniru A Asiru, Nov 11 2018

Mathematica

Binomial[Range[83,100],83] (* Harvey P. Dale, Oct 08 2016 *)

PARI

for(n=83, 100, print1(binomial(n,83), ", ")) \\ G. C. Greubel, Nov 10 2018

Sage

[binomial(n, 83) for n in range(83,99)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^83/(1-x)^84.

E.g.f.: x^83*exp(x)/83!. (End)

From Amiram Eldar, Dec 18 2020: (Start)

Sum_{n>=83} 1/a(n) = 83/82.

Sum_{n>=83} (-1)^(n+1)/a(n) = A001787(83)*log(2) - A242091(83)/82! = 401363372112056886002450432*log(2) - 1691854838361747589846883689013163648779313031899544168425629 / 6081348610273871795929269807305700 = 0.9883660041... (End)