Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Nov 03 2022 05:44:35
%S 5,110,1001,5720,24310,83980,248710,653752,1562275,3453450,7153575,
%T 14024400,26225628,47071640,81505820,136719440,222945905,354465254,
%U 550858165,838553320,1252716850,1839537700,2658968130,3787984200,5324436975,7391571330,10143295635
%N One half of binomial coefficients binomial(2*n-8,9).
%H Vincenzo Librandi, <a href="/A053133/b053133.txt">Table of n, a(n) for n = 9..200</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45, 10,-1).
%F a(n) = binomial(2*n-8, 9)/2.
%F G.f.: (5+60*x+126*x^2+60*x^3+5*x^4)/(1-x)^10.
%F a(n) = A053131(n)/2.
%F From _Amiram Eldar_, Nov 03 2022: (Start)
%F Sum_{n>=9} 1/a(n) = 223611/140 - 2304*log(2).
%F Sum_{n>=9} (-1)^(n+1)/a(n) = 144*log(2) - 13947/140. (End)
%t Table[Binomial[2*n-8,9]/2, {n,9,50}] (* _G. C. Greubel_, Aug 26 2018 *)
%o (PARI) a(n)=binomial(2*n-8,9)/2 \\ _Charles R Greathouse IV_, Oct 03 2011
%o (Magma) [Binomial(2*n-8,9)/2: n in [9..40]]; // _Vincenzo Librandi_, Oct 07 2011
%Y Cf. A053131.
%K nonn,easy
%O 9,1
%A _Wolfdieter Lang_