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A010965 a(n) = binomial(n,12).

%I A010965 #49 Dec 15 2023 15:55:02
%S A010965 1,13,91,455,1820,6188,18564,50388,125970,293930,646646,1352078,
%T A010965 2704156,5200300,9657700,17383860,30421755,51895935,86493225,
%U A010965 141120525,225792840,354817320,548354040,834451800,1251677700,1852482996,2707475148,3910797436,5586853480
%N A010965 a(n) = binomial(n,12).
%C A010965 Coordination sequence for 12-dimensional cyclotomic lattice Z[zeta_13].
%C A010965 In this sequence only 13 is prime. - _Artur Jasinski_, Dec 02 2007
%H A010965 T. D. Noe, <a href="/A010965/b010965.txt">Table of n, a(n) for n = 12..1000</a>
%H A010965 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 A010965 <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 A010965 a(n) = A110555(n+1,12). - _Reinhard Zumkeller_, Jul 27 2005
%F A010965 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 A010965 G.f.: x^12/(1-x)^13. - _Zerinvary Lajos_, Aug 06 2008, _R. J. Mathar_, Jul 07 2009
%F A010965 From _Amiram Eldar_, Dec 10 2020: (Start)
%F A010965 Sum_{n>=12} 1/a(n) = 12/11.
%F A010965 Sum_{n>=12} (-1)^n/a(n) = A001787(12)*log(2) - A242091(12)/11! = 24576*log(2) - 3934820/231 = 0.9322955884... (End)
%p A010965 seq(binomial(n,12),n=12..36); # _Zerinvary Lajos_, Aug 06 2008
%t A010965 Table[Binomial[n,12],{n,12,50}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 22 2011 *)
%o A010965 (Magma) [Binomial(n, 12): n in [12..100]]; // _Vincenzo Librandi_, Apr 22 2011
%o A010965 (PARI) for(n=12, 50, print1(binomial(n,12), ", ")) \\ _G. C. Greubel_, Aug 31 2017
%Y A010965 Cf. A000581, A010966, A010967, A001787, A242091.
%K A010965 nonn
%O A010965 12,2
%A A010965 _N. J. A. Sloane_
%E A010965 Some formulas referring to other offsets corrected by _R. J. Mathar_, Jul 07 2009