A010976 Binomial coefficient C(n,23).

1, 24, 300, 2600, 17550, 98280, 475020, 2035800, 7888725, 28048800, 92561040, 286097760, 834451800, 2310789600, 6107086800, 15471286560, 37711260990, 88732378800, 202112640600, 446775310800, 960566918220, 2012616400080, 4116715363800, 8233430727600

Offset: 23

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 23..1000
• Index entries for linear recurrences with constant coefficients, signature (24,-276,2024,-10626,42504,-134596,346104,-735471,1307504,-1961256,2496144,-2704156,2496144,-1961256,1307504,-735471,346104,-134596,42504,-10626,2024,-276,24,-1).

Crossrefs

Pascal's triangle A007318. [Zerinvary Lajos, Aug 04 2008]

Cf. A010970, A010971, A010972, A001787, A242091.

Programs

Magma

[Binomial(n,23): n in [23..90]]; // Vincenzo Librandi, Mar 26 2011

Maple

seq(binomial(n,23), n=23..43); # Zerinvary Lajos, Aug 04 2008

Mathematica

Table[Binomial[n,23],{n,23,50}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

PARI

for(n=23, 50, print1(binomial(n,23), ", ")) \\ G. C. Greubel, Nov 23 2017

Formula

a(n) = n/(n-23) * a(n-1) for n > 23. - Vincenzo Librandi, Mar 26 2011

G.f.: x^23/(1-x)^24. - G. C. Greubel, Nov 23 2017

From Amiram Eldar, Dec 11 2020: (Start)

Sum_{n>=23} 1/a(n) = 23/22.

Sum_{n>=23} (-1)^(n+1)/a(n) = A001787(23)*log(2) - A242091(23)/22! = 96468992*log(2) - 1945773591174209/29099070 = 0.9613305695... (End)