A010966 a(n) = binomial(n,13).

1, 14, 105, 560, 2380, 8568, 27132, 77520, 203490, 497420, 1144066, 2496144, 5200300, 10400600, 20058300, 37442160, 67863915, 119759850, 206253075, 347373600, 573166440, 927983760, 1476337800, 2310789600, 3562467300, 5414950296, 8122425444, 12033222880

Offset: 13

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 = 13..1000
• Milan Janjic, Two Enumerative Functions University of Banja Luka (Bosnia and Herzegovina, 2017).
• Ângela Mestre and José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
• Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Crossrefs

Cf. A000581, A001787, A110555, A242091.

Programs

Magma

[ Binomial(n,13): n in [13..50]]; // Vincenzo Librandi, Mar 26 2011

Maple

seq(binomial(n,13),n=13..36); # Zerinvary Lajos, Aug 06 2008

Mathematica

Table[Binomial[n,13],{n,13,50}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)

PARI

for(n=13, 50, print1(binomial(n,13), ", ")) \\ G. C. Greubel, Aug 31 2017

Formula

a(n) = -A110555(n+1,13). - Reinhard Zumkeller, Jul 27 2005

a(n+12) = 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)/13!. - Artur Jasinski, Dec 02 2007; R. J. Mathar, Jul 07 2009

G.f.: x^13/(1-x)^14. - Zerinvary Lajos, Aug 06 2008

a(n) = n/(n-13) * a(n-1), n > 13. - Vincenzo Librandi, Mar 26 2011

From Amiram Eldar, Dec 10 2020: (Start)

Sum_{n>=13} 1/a(n) = 13/12.

Sum_{n>=13} (-1)^(n+1)/a(n) = A001787(13)*log(2) - A242091(13)/12! = 53248*log(2) - 102308323/2772 = 0.9366404415... (End)

Extensions

Some formulas for different offsets rewritten by R. J. Mathar, Jul 07 2009