A017741 Binomial coefficients C(n,77).

1, 78, 3081, 82160, 1663740, 27285336, 377447148, 4529365776, 48124511370, 459856441980, 4000751045226, 32006008361808, 237377895350076, 1643385429346680, 10682005290753420, 65516299116620976, 380813488615359423, 2105674584108457986, 11113282527239083815

Offset: 77

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 77..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,77): n in [77..95]]; // G. C. Greubel, Nov 09 2018

Mathematica

Binomial[Range[77, 100], 77] (* Alonso del Arte, Nov 29 2017 *)

PARI

for(n=77, 95, print1(binomial(n,77), ", ")) \\ G. C. Greubel, Nov 09 2018

Sage

[binomial(n, 77) for n in range(77,93)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^77/(1-x)^78.

E.g.f.: x^77*exp(x)/77!. (End)

From Amiram Eldar, Dec 18 2020: (Start)

Sum_{n>=77} 1/a(n) = 77/76.

Sum_{n>=77} (-1)^(n+1)/a(n) = A001787(77)*log(2) - A242091(77)/76! = 5817955506895402903273472*log(2) - 1343868224767541359938872007600837410461932350790322871 / 333242841266582924868719919300 = 0.9874924526... (End)