A017746 Binomial coefficients C(n,82).

1, 83, 3486, 98770, 2123555, 36949857, 541931236, 6890268572, 77515521435, 783768050065, 7210666060598, 60962903966874, 477542747740513, 3489735464257595, 23929614612052080, 154744841157936784

Offset: 82

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 82..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,82): n in [82..100]]; // G. C. Greubel, Nov 09 2018

Mathematica

Array[Binomial[#, 82] &, 16, 82] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=82, 100, print1(binomial(n,82), ", ")) \\ G. C. Greubel, Nov 09 2018

Sage

[binomial(n, 82) for n in range(82,98)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^82/(1-x)^83.

E.g.f.: x^82*exp(x)/82!. (End)

From Amiram Eldar, Dec 18 2020: (Start)

Sum_{n>=82} 1/a(n) = 82/81.

Sum_{n>=82} (-1)^n/a(n) = A001787(82)*log(2) - A242091(82)/81! = 198263834416799184651812864*log(2) - 20383793233274067347552815456116292175605687562978728740013 / 148325575860338336486079751397700 = 0.9882289899... (End)