A010968 a(n) = binomial(n,15).

1, 16, 136, 816, 3876, 15504, 54264, 170544, 490314, 1307504, 3268760, 7726160, 17383860, 37442160, 77558760, 155117520, 300540195, 565722720, 1037158320, 1855967520, 3247943160, 5567902560, 9364199760, 15471286560, 25140840660, 40225345056, 63432274896

Offset: 15

Author

N. J. A. Sloane

Keywords

• nonn

Comments

There are no primes in this sequence. - Artur Jasinski, Dec 02 2007

Links

• T. D. Noe, Table of n, a(n) for n = 15..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 (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Crossrefs

Cf. A000581, A001787, A110555, A242091.

Programs

Magma

[ Binomial(n,15): n in [15..70]]; // Vincenzo Librandi, Mar 26 2011

Maple

seq(binomial(n,15),n=15..37); # Zerinvary Lajos, Aug 06 2008

Mathematica

Table[Binomial[n,15],{n,15,50}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)

PARI

for(n=15, 50, print1(binomial(n,15), ", ")) \\ G. C. Greubel, Aug 31 2017

Formula

a(n) = -A110555(n+1,15). - Reinhard Zumkeller, Jul 27 2005

a(n+14) = 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)(n+14)/15!. - Artur Jasinski, Dec 02 2007; R. J. Mathar, Jul 07 2009

G.f.: x^15/(1-x)^16. - Zerinvary Lajos, Aug 06 2008; R. J. Mathar, Jul 07 2009

a(n) = n/(n-15) * a(n-1), n > 15. - Vincenzo Librandi, Mar 26 2011

From Amiram Eldar, Dec 10 2020: (Start)

Sum_{n>=15} 1/a(n) = 15/14.

Sum_{n>=15} (-1)^(n+1)/a(n) = A001787(15)*log(2) - A242091(15)/14! = 245760*log(2) - 1023103525/6006 = 0.9438350048... (End)

Extensions

Some formulas adjusted to the offset by R. J. Mathar, Jul 07 2009