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 A113895 #25 Sep 06 2025 15:44:23
%S A113895 21,336,4950,72072,1051050,15402816,226972746,3362559200,50062040028,
%T A113895 748664904000,11241203533560,169398104243760,2561053271692500,
%U A113895 38833447762771200,590405728218941250,8998028449224091200,137437148161776305700,2103486475191421320000,32253916565936980114200
%N A113895 a(n) = C(2+2*n, n) * C(7+2*n, 2+n).
%H A113895 Robert Israel, <a href="/A113895/b113895.txt">Table of n, a(n) for n = 0..830</a>
%F A113895 a(n) = C(2+2*n, n) * C(7+2*n, 2+n).
%F A113895 From _Robert Israel_, Dec 16 2018: (Start)
%F A113895 a(n) = A001791(n+1)*A002054(n+3).
%F A113895 24*(11+2*n)*(5+2*n)*(n+3)*a(n+1) - 2*(n+4)*(11*n^2+112*n+252)*a(n+2)+(8+n)*(n+5)*(n+3)*a(n+3) = 0. (End)
%F A113895 a(n) ~ 2^(4*n+9) / (Pi*n). - _Amiram Eldar_, Sep 06 2025
%e A113895 If n=0 then C(2+2*0,0)*C(7+2*0,2+0) = C(2,0)*C(7,2) = 1*21 = 21.
%e A113895 If n=7 then C(2+2*7,7)*C(7+2*7,2+7) = C(16,7)*C(21,9) = 11440*293930 = 3362559200.
%e A113895 If n=10 then C(2+2*10,10)*C(7+2*10,2+10) = C(22,10)*C(27,12) = 646646*17383860 = 11241203533560.
%p A113895 seq(binomial(2+2*n,n)*binomial(7+2*n,2+n), n=0..20); # _Robert Israel_, Dec 16 2018
%t A113895 nmax = 10; NN[5, m_, x_] := x^m*(2*m+5)!*Hypergeometric2F1[-m, -m, -2*m-5, (x-1)/x]/((m+5)!*m!); tri = Table[CoefficientList[NN[5, m, x], x], {m, 0, 2*nmax+2}]; Table[tri[[2n+3, n+3]], {n, 0, nmax}] (* _Jean-François Alcover_, Sep 18 2013 *)
%o A113895 (PARI) a(n) = binomial(2+2*n,n)*binomial(7+2*n,2+n); \\ _Michel Marcus_, Sep 18 2013
%Y A113895 Cf. A001791, A002054, A062190.
%K A113895 easy,nonn,changed
%O A113895 0,1
%A A113895 _Zerinvary Lajos_, Jan 28 2006
%E A113895 Simpler name and more terms added by _Joerg Arndt_, Sep 18 2013