This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113888 #19 Sep 06 2025 15:44:38
%S A113888 6,84,1200,17325,252252,3699696,54609984,810616950,12092280200,
%T A113888 181176906768,2725140250560,41132585656890,622787147955000,
%U A113888 9456196695480000,143946539451475200,2196309308974461450,33581927605139911800,514470608092210770000,7895695609776494520000
%N A113888 a(n) = C(2*n+1,n)*C(2*n+6,n+1).
%F A113888 From _Amiram Eldar_, Sep 06 2025: (Start)
%F A113888 a(n) = A001700(n) * A002694(n+3).
%F A113888 a(n) ~ 2^(4*n+7) / (Pi*n). (End)
%e A113888 If n=0 then C(1+2*0,0+0)*C(6+2*0,1+0) = C(1,0)*C(6,1) = 1*6 = 6.
%e A113888 If n=4 then C(1+2*4,0+4)*C(6+2*4,1+4) = C(9,4)*C(14,5) = 126*2002 = 252252.
%e A113888 If n=10 then C(1+2*10,0+10)*C(6+2*10,1+10) = C(21,10)*C(26,11) = 352716*7726160 = 2725140250560.
%t A113888 Table[Binomial[2n+1,n]Binomial[2n+6,n+1],{n,0,20}] (* _Harvey P. Dale_, Jun 14 2011 *)
%Y A113888 Cf. A001700, A002694, A062190.
%K A113888 easy,nonn,changed
%O A113888 0,1
%A A113888 _Zerinvary Lajos_, Jan 28 2006
%E A113888 Edited by _N. J. A. Sloane_, Feb 03 2007