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

13,2

Comments

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

Links

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

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)

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 *)

Prog

(Magma) [ Binomial(n, 13): n in [13..50]]; // Vincenzo Librandi, Mar 26 2011
(PARI) for(n=13, 50, print1(binomial(n, 13), ", ")) \\ G. C. Greubel, Aug 31 2017

Crossrefs

Cf. A000581, A001787, A110555, A242091.

Sequence in context: A162632 A220893 A008506 * A290895 A341226 A022579

Adjacent sequences: A010963 A010964 A010965 * A010967 A010968 A010969

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved