A017734 Binomial coefficients C(n,70).

1, 71, 2556, 62196, 1150626, 17259390, 218618940, 2404808340, 23446881315, 205811513765, 1646492110120, 12124169174520, 82848489359220, 528955739755020, 3173734438530120, 17984495151670680

Offset: 70

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 70..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,70): n in [70..90]]; // G. C. Greubel, Nov 09 2018

Mathematica

Array[Binomial[#, 70] &, 16, 70] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=70, 90, print1(binomial(n,70), ", ")) \\ G. C. Greubel, Nov 09 2018

Sage

[binomial(n, 70) for n in range(70,86)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^70/(1-x)^71.

E.g.f.: x^70*exp(x)/70!. (End)

From Amiram Eldar, Dec 17 2020: (Start)

Sum_{n>=70} 1/a(n) = 70/69.

Sum_{n>=70} (-1)^n/a(n) = A001787(70)*log(2) - A242091(70)/69! = 41320706725109395619840*log(2) - 202565512367285681545862986460557640882612123732 / 7072489395972240350291181 = 0.9862914664... (End)