A010967 a(n) = binomial coefficient C(n,14).

1, 15, 120, 680, 3060, 11628, 38760, 116280, 319770, 817190, 1961256, 4457400, 9657700, 20058300, 40116600, 77558760, 145422675, 265182525, 471435600, 818809200, 1391975640, 2319959400, 3796297200, 6107086800, 9669554100, 15084504396, 23206929840, 35240152720

Offset

14,2

Comments

In this sequence there are no primes. - Artur Jasinski, Dec 02 2007

Links

T. D. Noe, Table of n, a(n) for n = 14..1000

Milan Janjic, Two Enumerative Functions.

Index entries for linear recurrences with constant coefficients, signature (15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1).

Formula

a(n) = A110555(n+1,14). - Reinhard Zumkeller, Jul 27 2005

a(n+13) = n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)(n+9)(n+10)(n+11)(n+12)(n+13)/14!. - Artur Jasinski, Dec 02 2007, R. J. Mathar, Jul 07 2009

G.f.: x^14/(1-x)^15. - Zerinvary Lajos, Aug 06 2008, R. J. Mathar, Jul 07 2009

a(n) = n/(n-14) * a(n-1), n > 14. - Vincenzo Librandi, Mar 26 2011

From Amiram Eldar, Dec 10 2020: (Start)

Sum_{n>=14} 1/a(n) = 14/13.

Sum_{n>=14} (-1)^n/a(n) = A001787(14)*log(2) - A242091(14)/13! = 114688*log(2) - 102309709/1287 = 0.9404563356... (End)

Maple

seq(binomial(n, 14), n=14..37); # Zerinvary Lajos, Aug 06 2008

Mathematica

Table[Binomial[n, 14], {n, 14, 50}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)

Prog

(Magma) [ Binomial(n, 14): n in [14..60]]; // Vincenzo Librandi, Mar 26 2011
(PARI) for(n=14, 50, print1(binomial(n, 14), ", ")) \\ G. C. Greubel, Aug 31 2017

Crossrefs

Cf. A000581, A001787, A110555, A242091.

Sequence in context: A126898 A162635 A247612 * A022580 A321950 A081079

Adjacent sequences: A010964 A010965 A010966 * A010968 A010969 A010970

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Some formulas rewritten for the correct offset by R. J. Mathar, Jul 07 2009

Status

approved