%I #39 Dec 15 2023 10:45:34
%S 1,33,561,6545,58905,435897,2760681,15380937,76904685,350343565,
%T 1471442973,5752004349,21090682613,73006209045,239877544005,
%U 751616304549,2254848913647,6499270398159,18053528883775,48459472266975,125994627894135,317986441828055
%N Binomial coefficient C(n,32).
%H T. D. Noe, <a href="/A010985/b010985.txt">Table of n, a(n) for n = 32..1000</a>
%H <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (33, -528, 5456, -40920, 237336, -1107568, 4272048, -13884156, 38567100, -92561040, 193536720, -354817320, 573166440, -818809200, 1037158320, -1166803110, 1166803110, -1037158320, 818809200, -573166440, 354817320, -193536720, 92561040, -38567100, 13884156, -4272048, 1107568, -237336, 40920, -5456, 528, -33, 1).
%F G.f.: x^32/(1-x)^33. - _Zerinvary Lajos_, Dec 19 2008; adapted to offset by _Enxhell Luzhnica_, Jan 21 2017
%F From _Amiram Eldar_, Dec 12 2020: (Start)
%F Sum_{n>=32} 1/a(n) = 32/31.
%F Sum_{n>=32} (-1)^n/a(n) = A001787(32)*log(2) - A242091(32)/31! = 68719476736*log(2) - 214947899422115237851136/4512611027925 = 0.9713417027... (End)
%p seq(binomial(n,32),n=32..55); # _Zerinvary Lajos_, Dec 19 2008
%t Table[Binomial[n,32],{n,32,60}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 26 2011 *)
%o (Magma) [Binomial(n, 32): n in [32..70]]; // _Vincenzo Librandi_, Jun 12 2013
%o (PARI) x='x+O('x^50); Vec(x^32/(1-x)^33) \\ _G. C. Greubel_, Nov 23 2017
%Y Cf. A010982, A010984, A001787, A242091.
%K nonn,easy
%O 32,2
%A _N. J. A. Sloane_