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%I #55 Mar 19 2024 15:30:37
%S 1,21,231,1771,10626,53130,230230,888030,3108105,10015005,30045015,
%T 84672315,225792840,573166440,1391975640,3247943160,7307872110,
%U 15905368710,33578000610,68923264410,137846528820,269128937220,513791607420,960566918220,1761039350070
%N a(n) = binomial(n,20).
%C In this sequence there are no primes. - _Artur Jasinski_, Dec 02 2007
%H T. D. Noe, <a href="/A010973/b010973.txt">Table of n, a(n) for n = 20..1000</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>.
%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).
%F a(n+19) = 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)/20!. - _Artur Jasinski_, Dec 02 2007; _R. J. Mathar_, Jul 07 2009
%F G.f.: x^20/(1-x)^21. - _Zerinvary Lajos_, Aug 04 2008; _R. J. Mathar_, Jul 07 2009
%F a(n) = n/(n-20) * a(n-1), n > 20. - _Vincenzo Librandi_, Mar 26 2011
%F From _Amiram Eldar_, Dec 11 2020: (Start)
%F Sum_{n>=20} 1/a(n) = 20/19.
%F Sum_{n>=20} (-1)^n/a(n) = A001787(20)*log(2) - A242091(20)/19! = 10485760*log(2) - 21149710469086/2909907 = 0.9562240549... (End)
%p seq(binomial(n,20),n=20..40); # _Zerinvary Lajos_, Aug 04 2008
%t Table[Binomial[n,20],{n,20,50}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 22 2011 *)
%o (Magma) [ Binomial(n,20): n in [20..80]]; // _Vincenzo Librandi_, Mar 26 2011
%o (PARI) for(n=20,50, print1(binomial(n,20), ", ")) \\ _G. C. Greubel_, Nov 23 2017
%Y Pascal's triangle A007318 diagonal. - _Zerinvary Lajos_, Aug 04 2008
%Y Cf. A001787, A242091.
%K nonn
%O 20,2
%A _N. J. A. Sloane_
%E Some formulas adjusted to the offset by _R. J. Mathar_, Jul 07 2009
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