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A010975 a(n) = binomial(n,22).

%I A010975 #44 Mar 19 2024 15:30:21
%S A010975 1,23,276,2300,14950,80730,376740,1560780,5852925,20160075,64512240,
%T A010975 193536720,548354040,1476337800,3796297200,9364199760,22239974430,
%U A010975 51021117810,113380261800,244662670200,513791607420,1052049481860,2104098963720,4116715363800
%N A010975 a(n) = binomial(n,22).
%C A010975 Coordination sequence for 22-dimensional cyclotomic lattice Z[zeta_23].
%H A010975 T. D. Noe, <a href="/A010975/b010975.txt">Table of n, a(n) for n = 22..1000</a>
%H A010975 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 A010975 Milan Janjic, <a href="https://pmf.unibl.org/janjic/">Two Enumerative Functions</a>.
%H A010975 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (23, -253, 1771, -8855, 33649, -100947, 245157, -490314, 817190, -1144066, 1352078, -1352078, 1144066, -817190, 490314, -245157, 100947, -33649, 8855, -1771, 253, -23, 1).
%F A010975 a(n) = n/(n-22) * a(n-1), n > 22. - _Vincenzo Librandi_, Mar 26 2011
%F A010975 G.f.: x^22/(1-x)^23. - _G. C. Greubel_, Nov 23 2017
%F A010975 From _Amiram Eldar_, Dec 11 2020: (Start)
%F A010975 Sum_{n>=22} 1/a(n) = 22/21.
%F A010975 Sum_{n>=22} (-1)^n/a(n) = A001787(22)*log(2) - A242091(22)/21! = 46137344*log(2) - 42299425233749/1322685 = 0.9597667941... (End)
%p A010975 seq(binomial(n,22),n=22..42); # _Zerinvary Lajos_, Aug 04 2008
%t A010975 Binomial[Range[22,50],22]  (* _Harvey P. Dale_, Apr 02 2011 *)
%o A010975 (Magma) [ Binomial(n,22): n in [22..80]]; // _Vincenzo Librandi_, Mar 26 2011
%o A010975 (PARI) for(n=22, 50, print1(binomial(n,22), ", ")) \\ _G. C. Greubel_, Nov 23 2017
%Y A010975 Pascal's triangle A007318. - _Zerinvary Lajos_, Aug 04 2008
%Y A010975 Cf. A001787, A242091.
%K A010975 nonn
%O A010975 22,2
%A A010975 _N. J. A. Sloane_