A017742 Binomial coefficients C(n,78).

1, 79, 3160, 85320, 1749060, 29034396, 406481544, 4935847320, 53060358690, 512916800670, 4513667845896, 36519676207704, 273897571557780, 1917283000904460, 12599288291657880, 78115587408278856

Offset: 78

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 78..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,78): n in [78..100]]; // G. C. Greubel, Nov 09 2018

Maple

seq(binomial(n,78),n=78..100); # Robert Israel, Jul 06 2018

Mathematica

Binomial[Range[78,98],78] (* Harvey P. Dale, Sep 18 2016 *)

PARI

for(n=78, 100, print1(binomial(n,78), ", ")) \\ G. C. Greubel, Nov 09 2018

Sage

[binomial(n, 78) for n in range(78,94)] # Zerinvary Lajos, May 23 2009

Formula

G.f.: x^78/(1-x)^79. - Robert Israel, Jul 06 2018

E.g.f.: x^78*exp(x)/78!. - G. C. Greubel, Nov 09 2018

From Amiram Eldar, Dec 18 2020: (Start)

Sum_{n>=78} 1/a(n) = 78/77.

Sum_{n>=78} (-1)^n/a(n) = A001787(78)*log(2) - A242091(78)/77! = 11787026741242634453385216*log(2) - 1343868224767541359938872174222258043753394785150282521 / 164485248573890289839047652475 = 0.9876470468... (End)