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A010974 a(n) = binomial(n,21).

%I A010974 #45 May 07 2025 11:14:11
%S A010974 1,22,253,2024,12650,65780,296010,1184040,4292145,14307150,44352165,
%T A010974 129024480,354817320,927983760,2319959400,5567902560,12875774670,
%U A010974 28781143380,62359143990,131282408400,269128937220,538257874440,1052049481860,2012616400080,3773655750150
%N A010974 a(n) = binomial(n,21).
%C A010974 In this sequence there are no primes. - _Artur Jasinski_, Dec 02 2007
%H A010974 T. D. Noe, <a href="/A010974/b010974.txt">Table of n, a(n) for n = 21..1000</a>
%H A010974 Milan Janjic, <a href="https://pmf.unibl.org/janjic/">Two Enumerative Functions</a>.
%H A010974 <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (22,-231,1540,-7315,26334,-74613,170544,-319770,497420,-646646,705432,-646646,497420,-319770,170544,-74613,26334,-7315,1540,-231,22,-1).
%F A010974 a(n) = 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)*(n+18)*(n+19)*(n+20) / 21!. - _Artur Jasinski_, Dec 02 2007
%F A010974 a(n) = n/(n-21) * a(n-1), n > 21. - _Vincenzo Librandi_, Mar 26 2011
%F A010974 From _Amiram Eldar_, Dec 11 2020: (Start)
%F A010974 Sum_{n>=21} 1/a(n) = 21/20.
%F A010974 Sum_{n>=21} (-1)^(n+1)/a(n) = A001787(21)*log(2) - A242091(21)/20! = 22020096*log(2) - 42299423848079/2771340 = 0.9580705153... (End)
%p A010974 seq(binomial(n,21),n=21..41); # _Zerinvary Lajos_, Aug 04 2008
%t A010974 Table[Binomial[n,21],{n,21,50}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 22 2011 *)
%o A010974 (Magma) [ Binomial(n,21): n in [21..80]]; // _Vincenzo Librandi_, Mar 26 2011
%o A010974 (PARI) for(n=21, 50, print1(binomial(n,21), ", ")) \\ _G. C. Greubel_, Nov 23 2017
%Y A010974 Pascal's triangle A007318. - _Zerinvary Lajos_, Aug 04 2008
%Y A010974 Cf. A001787, A242091.
%K A010974 nonn
%O A010974 21,2
%A A010974 _N. J. A. Sloane_