A017738 Binomial coefficients C(n,74).

1, 75, 2850, 73150, 1426425, 22537515, 300500200, 3477216600, 35641470150, 328693558050, 2761025887620, 21335200040700, 152902266958350, 1023269017336650, 6431976680401800, 38163061637050680

Offset: 74

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 74..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,74): n in [74..90]]; // G. C. Greubel, Nov 09 2018

Mathematica

Binomial[Range[74,90],74] (* Harvey P. Dale, Jul 25 2017 *)

PARI

for(n=74, 90, print1(binomial(n,74), ", ")) \\ G. C. Greubel, Nov 09 2018

Sage

[binomial(n, 74) for n in range(74,90)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^74/(1-x)^75.

E.g.f.: x^74*exp(x)/74!. (End)

From Amiram Eldar, Dec 18 2020: (Start)

Sum_{n>=74} 1/a(n) = 74/73.

Sum_{n>=74} (-1)^n/a(n) = A001787(74)*log(2) - A242091(74)/73! = 698910239464707491627008*log(2) - 6719341123837706799694347993519215590602682862640625 / 13870107447311829845887261506 = 0.9870045330... (End)