A010965 - OEIS

%I #49 Dec 15 2023 15:55:02

%S 1,13,91,455,1820,6188,18564,50388,125970,293930,646646,1352078,

%T 2704156,5200300,9657700,17383860,30421755,51895935,86493225,

%U 141120525,225792840,354817320,548354040,834451800,1251677700,1852482996,2707475148,3910797436,5586853480

%N a(n) = binomial(n,12).

%C Coordination sequence for 12-dimensional cyclotomic lattice Z[zeta_13].

%C In this sequence only 13 is prime. - _Artur Jasinski_, Dec 02 2007

%H T. D. Noe, <a href="/A010965/b010965.txt">Table of n, a(n) for n = 12..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 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).

%F a(n) = A110555(n+1,12). - _Reinhard Zumkeller_, Jul 27 2005

%F a(n+11) = n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)(n+9)(n+10)(n+11)/12!. - _Artur Jasinski_, Dec 02 2007, _R. J. Mathar_, Jul 07 2009

%F G.f.: x^12/(1-x)^13. - _Zerinvary Lajos_, Aug 06 2008, _R. J. Mathar_, Jul 07 2009

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

%F Sum_{n>=12} 1/a(n) = 12/11.

%F Sum_{n>=12} (-1)^n/a(n) = A001787(12)*log(2) - A242091(12)/11! = 24576*log(2) - 3934820/231 = 0.9322955884... (End)

%p seq(binomial(n,12),n=12..36); # _Zerinvary Lajos_, Aug 06 2008

%t Table[Binomial[n,12],{n,12,50}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 22 2011 *)

%o (Magma) [Binomial(n, 12): n in [12..100]]; // _Vincenzo Librandi_, Apr 22 2011

%o (PARI) for(n=12, 50, print1(binomial(n,12), ", ")) \\ _G. C. Greubel_, Aug 31 2017

%Y Cf. A000581, A010966, A010967, A001787, A242091.

%K nonn

%O 12,2

%A _N. J. A. Sloane_

%E Some formulas referring to other offsets corrected by _R. J. Mathar_, Jul 07 2009