A017728 Binomial coefficients C(n,64).

1, 65, 2145, 47905, 814385, 11238513, 131115985, 1329890705, 11969016345, 97082021465, 718406958841, 4898229264825, 31022118677225, 183746395242025, 1023729916348425, 5391644226101705, 26958221130508525

Offset: 64

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 64..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,64): n in [64..90]]; // G. C. Greubel, Nov 08 2018

Mathematica

Array[Binomial[#, 64] &, 17, 64] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=64, 90, print1(binomial(n,64), ", ")) \\ G. C. Greubel, Nov 08 2018

Sage

[binomial(n, 64) for n in range(64,81)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 08 2018: (Start)

G.f.: x^64/(1-x)^65.

E.g.f.: x^64*exp(x)/64!. (End)

From Amiram Eldar, Dec 17 2020: (Start)

Sum_{n>=64} 1/a(n) = 64/63.

Sum_{n>=64} (-1)^n/a(n) = A001787(64)*log(2) - A242091(64)/63! = 590295810358705651712*log(2) - 1511682928114072250338673755441561389600833536 / 3694584012821319585973005 = 0.9850618563... (End)