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a(n) = binomial(n,16).
4

%I #48 Dec 15 2023 10:14:06

%S 1,17,153,969,4845,20349,74613,245157,735471,2042975,5311735,13037895,

%T 30421755,67863915,145422675,300540195,601080390,1166803110,

%U 2203961430,4059928950,7307872110,12875774670,22239974430,37711260990,62852101650,103077446706,166509721602

%N a(n) = binomial(n,16).

%C a(n) = A110555(n+1,16). - _Reinhard Zumkeller_, Jul 27 2005

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

%C In this sequence only 17 is prime. - _Artur Jasinski_, Dec 02 2007

%H T. D. Noe, <a href="/A010969/b010969.txt">Table of n, a(n) for n = 16..1000</a>

%H Matthias Beck and Serkan Hosten, <a href="http://arxiv.org/abs/math/0508136">Cyclotomic polytopes and growth series of cyclotomic lattices</a>, arXiv:math/0508136 [math.CO], 2005-2006.

%H Milan Janjic, <a href="https://pmf.unibl.org/janjic/">Two Enumerative Functions</a>.

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

%F 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

%F G.f.: x^16/(1-x)^17. - _Zerinvary Lajos_, Aug 06 2008; _R. J. Mathar_, Jul 07 2009

%F a(n) = n/(n-16) * a(n-1), n > 16. - _Vincenzo Librandi_, Mar 26 2011

%F From _Amiram Eldar_, Dec 10 2020: (Start)

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

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

%p seq(binomial(n,16),n=16..37); # _Zerinvary Lajos_, Aug 06 2008

%t Table[Binomial[n,16],{n,16,50}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 22 2011 *)

%o (Magma) [ Binomial(n,16): n in [16..80]]; // _Vincenzo Librandi_, Mar 26 2011

%o (PARI) for(n=16, 50, print1(binomial(n,16), ", ")) \\ _G. C. Greubel_, Aug 31 2017

%K nonn

%O 16,2

%A _N. J. A. Sloane_

%E Some formulas adjusted to the offset by _R. J. Mathar_, Jul 07 2009