%I #23 Sep 07 2025 01:44:41

%S 1,48,1326,27720,487635,7624512,109453344,1473109704,18855883575,

%T 231900297200,2761025887620,32006008361808,362827605867363,

%U 4036320536972640,44186942677323600,477092811067148640,5089954010045192190,53739140249027550240,562196697805477054650

%N Binomial coefficient C(4n,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="/A004341/b004341.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].

%F D-finite with recurrence -3*(3*n+10)*(n-11)*(n+3)*(3*n+11)*a(n) + 8*n*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1) = 0. - _R. J. Mathar_, Mar 19 2025

%F a(n) ~ 2^(8*n+1/2) / (3^(3*n+23/2) * sqrt(Pi*n)). - _Amiram Eldar_, Sep 07 2025

%t Table[Binomial[4n,n-11],{n,11,30}] (* _Harvey P. Dale_, Jul 02 2017 *)

%K nonn,easy

%O 11,2

%A _N. J. A. Sloane_