A053133 - 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_