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 A359761 #17 Aug 24 2025 11:29:56 %S A359761 1,6,210,13860,1351350,174594420,28109701620,5421156741000, %T A359761 1218404977539750,312723944235202500,90252130306279441500, %U A359761 28929910132721937339000,10197793321784482911997500,3920659309406065045704885000,1632674555274097086889962825000,732091270584905133761459330730000 %N A359761 a(n) = binomial(4*n, 2*n)*(2*n)!/(2^n*n!). %F A359761 a(n) = (2^(3*n)*Gamma(2*n + 1/2))/(sqrt(Pi)*Gamma(n + 1)). %F A359761 a(n) = A359760(4*n, 2*n), the central terms of the triangle without the zeros. %F A359761 From _R. J. Mathar_, Jan 25 2023: (Start) %F A359761 a(n) = A001448(n)*A001147(n). %F A359761 D-finite with recurrence n*a(n) -2*(4*n-1)*(4*n-3)*a(n-1)=0. (End) %F A359761 From _Stefano Spezia_, Aug 24 2025: (Start) %F A359761 E.g.f.: 2*EllipticK(8*sqrt(2*x)/(1 + 4*sqrt(2*x)))/(Pi*sqrt(1 + 4*sqrt(2*x))). %F A359761 E.g.f.: hypergeom([1/2, 1/2], [1], 8*sqrt(2*x)/(1 + 4*sqrt(2*x)))/sqrt(1 + 4*sqrt(2*x)). (End) %p A359761 a := binomial(4*n, 2*n)*(2*n)!/(2^n*n!): %p A359761 seq(a(n), n = 0..15); %Y A359761 Cf. A359760. %K A359761 nonn,easy,changed %O A359761 0,2 %A A359761 _Peter Luschny_, Jan 14 2023