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

15,2

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).

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)

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 *)

Prog

(Magma) [ Binomial(n, 15): n in [15..70]]; // Vincenzo Librandi, Mar 26 2011
(PARI) for(n=15, 50, print1(binomial(n, 15), ", ")) \\ G. C. Greubel, Aug 31 2017

Crossrefs

Cf. A000581, A001787, A110555, A242091.

Sequence in context: A302817 A303510 A162636 * A290896 A223031 A341227

Adjacent sequences: A010965 A010966 A010967 * A010969 A010970 A010971

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved