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A010972 a(n) = binomial(n,19).

%I A010972 #46 May 07 2025 11:12:42
%S A010972 1,20,210,1540,8855,42504,177100,657800,2220075,6906900,20030010,
%T A010972 54627300,141120525,347373600,818809200,1855967520,4059928950,
%U A010972 8597496600,17672631900,35345263800,68923264410,131282408400,244662670200,446775310800,800472431850
%N A010972 a(n) = binomial(n,19).
%C A010972 In this sequence there are no primes. - _Artur Jasinski_, Dec 02 2007
%H A010972 T. D. Noe, <a href="/A010972/b010972.txt">Table of n, a(n) for n = 19..1000</a>
%H A010972 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (20,-190,1140,-4845,15504,-38760,77520,-125970,167960,-184756,167960,-125970,77520,-38760,15504,-4845,1140,-190,20,-1).
%F A010972 a(n+18) = 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)/19!. - _Artur Jasinski_, Dec 02 2007; _R. J. Mathar_, Jul 07 2009
%F A010972 G.f.: x^19/(1-x)^20. - _Zerinvary Lajos_, Aug 04 2008; _R. J. Mathar_, Jul 07 2009
%F A010972 a(n) = n/(n-19) * a(n-1), n > 19. - _Vincenzo Librandi_, Mar 26 2011
%F A010972 From _Amiram Eldar_, Dec 11 2020: (Start)
%F A010972 Sum_{n>=19} 1/a(n) = 19/18.
%F A010972 Sum_{n>=19} (-1)^(n+1)/a(n) = A001787(19)*log(2) - A242091(19)/18! = 4980736*log(2) - 10574853703013/3063060 = 0.9542064261... (End)
%p A010972 seq(binomial(n,19),n=19..39); # _Zerinvary Lajos_, Aug 04 2008
%t A010972 Table[Binomial[n,19],{n,19,50}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 22 2011 *)
%o A010972 (Magma) [ Binomial(n,19): n in [19..45]]; // _Vincenzo Librandi_, Mar 26 2011
%o A010972 (PARI) vector(25, n, binomial(n+18,19)) \\ _G. C. Greubel_, Nov 23 2017
%o A010972 (SageMath) [binomial(n,19) for n in (19..45)] # _G. C. Greubel_, Aug 27 2019
%o A010972 (GAP) List([19..45], n-> Binomial(n,19) ); # _G. C. Greubel_, Aug 27 2019
%Y A010972 Cf. A001787, A242091.
%K A010972 nonn
%O A010972 19,2
%A A010972 _N. J. A. Sloane_