This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A010971 #46 Mar 19 2024 15:31:27
%S A010971 1,19,190,1330,7315,33649,134596,480700,1562275,4686825,13123110,
%T A010971 34597290,86493225,206253075,471435600,1037158320,2203961430,
%U A010971 4537567650,9075135300,17672631900,33578000610,62359143990,113380261800,202112640600,353697121050,608359048206
%N A010971 a(n) = binomial(n,18).
%C A010971 Coordination sequence for 18-dimensional cyclotomic lattice Z[zeta_19].
%C A010971 Product of 18 consecutive numbers divided by 18!. - _Artur Jasinski_, Dec 02 2007
%C A010971 In this sequence only 19 is prime. - _Artur Jasinski_, Dec 02 2007
%C A010971 With a different offset, number of n-permutations (n>=18) of 2 objects: u,v, with repetition allowed, containing exactly (18) u's. - _Zerinvary Lajos_, Aug 04 2008
%H A010971 T. D. Noe, <a href="/A010971/b010971.txt">Table of n, a(n) for n = 18..1000</a>
%H A010971 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 A010971 Milan Janjic, <a href="https://pmf.unibl.org/janjic/">Two Enumerative Functions</a>.
%H A010971 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).
%F A010971 a(n+17) = 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)*(n+16)*(n+17)/18!. - _Artur Jasinski_, Dec 02 2007; _R. J. Mathar_, Jul 07 2009
%F A010971 G.f.: x^18/(1-x)^19. - _Zerinvary Lajos_, Aug 04 2008; _R. J. Mathar_, Jul 07 2009
%F A010971 From _Amiram Eldar_, Dec 10 2020: (Start)
%F A010971 Sum_{n>=18} 1/a(n) = 18/17.
%F A010971 Sum_{n>=18} (-1)^n/a(n) = A001787(18)*log(2) - A242091(18)/17! = 2359296*log(2) - 556571077357/340340 = 0.9519925176... (End)
%p A010971 seq(binomial(n,18),n=18..38); # _Zerinvary Lajos_, Aug 04 2008
%t A010971 Table[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)(n+16)(n+17)/18!,{n,1,100}] (* _Artur Jasinski_, Dec 02 2007 *)
%t A010971 Table[Binomial[n, 18], {n, 18, 50}] (* _Vincenzo Librandi_, Aug 08 2017 *)
%o A010971 (Magma) [Binomial(n, 18): n in [18..50]]; // _Vincenzo Librandi_, Aug 08 2017
%o A010971 (PARI) for(n=18,50, print1(binomial(n,18), ", ")) \\ _G. C. Greubel_, Nov 23 2017
%Y A010971 Cf. A001787, A242091.
%K A010971 nonn
%O A010971 18,2
%A A010971 _N. J. A. Sloane_
%E A010971 Some formulas adjusted to the offset by _R. J. Mathar_, Jul 07 2009