A017745 Binomial coefficients C(n,81).

1, 82, 3403, 95284, 2024785, 34826302, 504981379, 6348337336, 70625252863, 706252528630, 6426898010533, 53752237906276, 416579843773639, 3012192716517082, 20439879147794485, 130815226545884704

Offset: 81

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 81..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,81): n in [81..100]]; // G. C. Greubel, Nov 09 2018

Mathematica

Table[Binomial[n,81],{n,81,100}]  (* Harvey P. Dale, Jan 23 2011 *)

PARI

for(n=81, 100, print1(binomial(n,81), ", ")) \\ G. C. Greubel, Nov 09 2018

Sage

[binomial(n, 81) for n in range(81,97)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^81/(1-x)^82.

E.g.f.: x^81*exp(x)/81!. (End)

From Amiram Eldar, Dec 18 2020: (Start)

Sum_{n>=81} 1/a(n) = 81/80.

Sum_{n>=81} (-1)^(n+1)/a(n) = A001787(81)*log(2) - A242091(81)/80! = 97922991388784963151200256*log(2) - 20383793233274067347552815305959536366374285194354782880613 / 300313511618462804737247891718800 = 0.9880887084... (End)