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

Author

N. J. A. Sloane

Keywords

• nonn

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).

Crossrefs

Cf. A000581, A001787, A110555, A242091.

Programs

Magma

[ Binomial(n,14): n in [14..60]]; // Vincenzo Librandi, Mar 26 2011

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 *)

PARI

for(n=14, 50, print1(binomial(n,14), ", ")) \\ G. C. Greubel, Aug 31 2017

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)

Extensions

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