A010969 a(n) = binomial(n,16).

1, 17, 153, 969, 4845, 20349, 74613, 245157, 735471, 2042975, 5311735, 13037895, 30421755, 67863915, 145422675, 300540195, 601080390, 1166803110, 2203961430, 4059928950, 7307872110, 12875774670, 22239974430, 37711260990, 62852101650, 103077446706, 166509721602

Offset: 16

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) = A110555(n+1,16). - Reinhard Zumkeller, Jul 27 2005

Coordination sequence for 16-dimensional cyclotomic lattice Z[zeta_17].

In this sequence only 17 is prime. - Artur Jasinski, Dec 02 2007

Links

• T. D. Noe, Table of n, a(n) for n = 16..1000
• Matthias Beck and Serkan Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.
• Milan Janjic, Two Enumerative Functions.
• Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

Programs

Magma

[ Binomial(n,16): n in [16..80]]; // Vincenzo Librandi, Mar 26 2011

Maple

seq(binomial(n,16),n=16..37); # Zerinvary Lajos, Aug 06 2008

Mathematica

Table[Binomial[n,16],{n,16,50}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)

PARI

for(n=16, 50, print1(binomial(n,16), ", ")) \\ G. C. Greubel, Aug 31 2017

Formula

a(n+15) = 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)(n+15)/16!. - Artur Jasinski, Dec 02 2007

G.f.: x^16/(1-x)^17. - Zerinvary Lajos, Aug 06 2008; R. J. Mathar, Jul 07 2009

a(n) = n/(n-16) * a(n-1), n > 16. - Vincenzo Librandi, Mar 26 2011

From Amiram Eldar, Dec 10 2020: (Start)

Sum_{n>=16} 1/a(n) = 16/15.

Sum_{n>=16} (-1)^n/a(n) = A001787(16)*log(2) - A242091(16)/15! = 524288*log(2) - 16369704448/45045 = 0.9468480104... (End)

Extensions

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