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a(n) = binomial coefficient C(n,44).
5

%I #26 Dec 15 2023 11:06:07

%S 1,45,1035,16215,194580,1906884,15890700,115775100,752538150,

%T 4431613550,23930713170,119653565850,558383307300,2448296039700,

%U 10142940735900,39895566894540,149608375854525,536830054536825,1849081298960175,6131164307078475,19619725782651120

%N a(n) = binomial coefficient C(n,44).

%H T. D. Noe, <a href="/A010997/b010997.txt">Table of n, a(n) for n = 44..1000</a>

%H <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (45, -990, 14190, -148995, 1221759, -8145060, 45379620, -215553195, 886163135, -3190187286, 10150595910, -28760021745, 73006209045, -166871334960, 344867425584, -646626422970, 1103068603890, -1715884494940, 2438362177020, -3169870830126, 3773655750150, -4116715363800, 4116715363800, -3773655750150, 3169870830126, -2438362177020, 1715884494940, -1103068603890, 646626422970, -344867425584, 166871334960, -73006209045, 28760021745, -10150595910, 3190187286, -886163135, 215553195, -45379620, 8145060, -1221759, 148995, -14190, 990, -45, 1).

%F G.f.: x^44/(1-x)^45. - _Zerinvary Lajos_, Dec 20 2008

%F From _Amiram Eldar_, Dec 15 2020: (Start)

%F Sum_{n>=44} 1/a(n) = 44/43.

%F Sum_{n>=44} (-1)^n/a(n) = A001787(44)*log(2) - A242091(44)/43! = 387028092977152*log(2) - 7178888410874815560070307159852/26760193632961425 = 0.9786869603... (End)

%p seq(binomial(n,44),n=44..67); # _Zerinvary Lajos_, Dec 20 2008

%t Table[Binomial[n,44],{n,44,70}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)

%o (Magma) [Binomial(n, 44): n in [44..70]]; // _Vincenzo Librandi_, Jun 12 2013

%Y Cf. A010995, A010996, A001787, A242091.

%K nonn

%O 44,2

%A _N. J. A. Sloane_