A004329 - OEIS

%I #28 Jan 14 2025 01:53:10

%S 1,36,741,11480,148995,1712304,18009460,177100560,1652411475,

%T 14783142660,127805525001,1074082795968,8815083648488,70907466006720,

%U 560658857389200,4367914309753280,33594090947249085,255485622301674660,1923856105133987325,14360771909211532200

%N Binomial coefficient C(3n,n-11).

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.

%H Seiichi Manyama, <a href="/A004329/b004329.txt">Table of n, a(n) for n = 11..1000</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H Milan Janjic, <a href="https://old.pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>.

%F D-finite with recurrence -2*(n+5)*(n-11)*(2*n+11)*a(n) +3*n*(3*n-1)*(3*n-2)*a(n-1)=0. - _R. J. Mathar_, Jan 13 2025

%F a(n) ~ 3^(3*n)/(2^(2*n+12)*sqrt(n*Pi/3)). - _Stefano Spezia_, Jan 13 2025

%t Table[Binomial[3*n, n - 11], {n, 11, 30}] (* _Paolo Xausa_, Jan 13 2025 *)

%K nonn,easy

%O 11,2

%A _N. J. A. Sloane_