A017747 Binomial coefficients C(n,83).

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

Offset

83,2

Links

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

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)

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 *)

Prog

(Sage) [binomial(n, 83) for n in range(83, 99)] # Zerinvary Lajos, May 23 2009
(PARI) for(n=83, 100, print1(binomial(n, 83), ", ")) \\ G. C. Greubel, Nov 10 2018
(Magma) [Binomial(n, 83): n in [83..100]]; // G. C. Greubel, Nov 10 2018
(GAP) List([83..100], n->Binomial(n, 83)); # Muniru A Asiru, Nov 11 2018

Crossrefs

Cf. A001787, A242091.

Sequence in context: A017800 A035737 A035806 * A223959 A143402 A004379

Adjacent sequences: A017744 A017745 A017746 * A017748 A017749 A017750

Keyword

nonn

Author

N. J. A. Sloane

Status

approved