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a(n) = binomial coefficient C(n,14).
8

%I #43 Dec 15 2023 10:23:47

%S 1,15,120,680,3060,11628,38760,116280,319770,817190,1961256,4457400,

%T 9657700,20058300,40116600,77558760,145422675,265182525,471435600,

%U 818809200,1391975640,2319959400,3796297200,6107086800,9669554100,15084504396,23206929840,35240152720

%N a(n) = binomial coefficient C(n,14).

%C In this sequence there are no primes. - _Artur Jasinski_, Dec 02 2007

%H T. D. Noe, <a href="/A010967/b010967.txt">Table of n, a(n) for n = 14..1000</a>

%H Milan Janjic, <a href="https://pmf.unibl.org/janjic/">Two Enumerative Functions</a>.

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1).

%F a(n) = A110555(n+1,14). - _Reinhard Zumkeller_, Jul 27 2005

%F a(n+13) = 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)/14!. - _Artur Jasinski_, Dec 02 2007, _R. J. Mathar_, Jul 07 2009

%F G.f.: x^14/(1-x)^15. - _Zerinvary Lajos_, Aug 06 2008, _R. J. Mathar_, Jul 07 2009

%F a(n) = n/(n-14) * a(n-1), n > 14. - _Vincenzo Librandi_, Mar 26 2011

%F From _Amiram Eldar_, Dec 10 2020: (Start)

%F Sum_{n>=14} 1/a(n) = 14/13.

%F Sum_{n>=14} (-1)^n/a(n) = A001787(14)*log(2) - A242091(14)/13! = 114688*log(2) - 102309709/1287 = 0.9404563356... (End)

%p seq(binomial(n,14),n=14..37); # _Zerinvary Lajos_, Aug 06 2008

%t Table[Binomial[n,14],{n,14,50}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 22 2011 *)

%o (Magma) [ Binomial(n,14): n in [14..60]]; // _Vincenzo Librandi_, Mar 26 2011

%o (PARI) for(n=14, 50, print1(binomial(n,14), ", ")) \\ _G. C. Greubel_, Aug 31 2017

%Y Cf. A000581, A001787, A110555, A242091.

%K nonn

%O 14,2

%A _N. J. A. Sloane_

%E Some formulas rewritten for the correct offset by _R. J. Mathar_, Jul 07 2009