A017739 Binomial coefficients C(n,75).

1, 76, 2926, 76076, 1502501, 24040016, 324540216, 3801756816, 39443226966, 368136785016, 3129162672636, 24464362713336, 177366629671686, 1200635647008336, 7632612327410136, 45795673964460816

Offset: 75

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 75..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,75): n in [75..95]]; // G. C. Greubel, Nov 09 2018

Mathematica

Array[Binomial[#, 75] &, 15, 76] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=75, 95, print1(binomial(n,75), ", ")) \\ G. C. Greubel, Nov 09 2018

Sage

[binomial(n, 75) for n in range(75,91)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^75/(1-x)^76.

E.g.f.: x^75*exp(x)/75!. (End)

From Amiram Eldar, Dec 18 2020: (Start)

Sum_{n>=75} 1/a(n) = 75/74.

Sum_{n>=75} (-1)^(n+1)/a(n) = A001787(75)*log(2) - A242091(75)/74! = 1416709944860893564108800*log(2) - 83991764047971334996179436607161740581470072578392225 / 85532329258422950716304779287 = 0.9871713508... (End)