A017717 Binomial coefficients C(n,53).

1, 54, 1485, 27720, 395010, 4582116, 45057474, 386206920, 2944827765, 20286591270, 127805525001, 743595781824, 4027810484880, 20448884000160, 97862516286480, 443643407165376, 1913212193400684, 7877932561061640

Offset

53,2

Links

G. C. Greubel, Table of n, a(n) for n = 53..10000

Formula

From G. C. Greubel, Nov 03 2018: (Start)

G.f.: x^53/(1-x)^54.

E.g.f.: x^53*exp(x)/53!. (End)

From Amiram Eldar, Dec 16 2020: (Start)

Sum_{n>=53} 1/a(n) = 53/52.

Sum_{n>=53} (-1)^(n+1)/a(n) = A001787(53)*log(2) - A242091(53)/52! = 238690780250636288*log(2) - 12818255587371480560673756439003166003 / 77476112606149917660 = 0.9821211403... (End)

Mathematica

Table[Binomial[n, 53], {n, 53, 80}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

Prog

(Sage) [binomial(n, 53) for n in range(53, 71)] # Zerinvary Lajos, May 23 2009
(PARI) for(n=53, 80, print1(binomial(n, 53), ", ")) \\ G. C. Greubel, Nov 03 2018
(Magma) [Binomial(n, 53): n in [53..80]]; // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A017713, A017715, A017716, A001787, A242091.

Sequence in context: A079876 A017770 A035722 * A172501 A173188 A004363

Adjacent sequences: A017714 A017715 A017716 * A017718 A017719 A017720

Keyword

nonn

Author

N. J. A. Sloane

Status

approved