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 A091535 #18 Sep 01 2025 05:15:01 %S A091535 1,20,1120,123200,22422400,6098892800,2317579264000,1172695107584000, %T A091535 762251819929600000,618948477782835200000,613996889960572518400000, %U A091535 730656299053081296896000000,1027302756468632303435776000000,1684776520608556977634672640000000 %N A091535 First column (k=2) of array A091534 ((5,2)-Stirling2). %C A091535 The scaled sequence (2/(3n-1)!!!)*a(n) = (3*n-2)!!! = A007559(n), n>=1. %F A091535 a(n) = (3*n-1)!/(2!*3^(n-(2-1))*(n-1)!) = ((3*n-1)!/2)/A032031(n-1). %F A091535 a(n) = A091534(n, 2), n>=1. %F A091535 E.g.f.: (hypergeom([1/3, 2/3, 1], [], 9*x)-1)/2. %F A091535 a(n) = 9^n*Gamma(n+1/3)*Gamma(n+2/3)*sqrt(3)/(4*Pi). - _Peter Luschny_, Sep 17 2014 %F A091535 a(n) ~ (sqrt(3)/2) * (3*n/e)^(2*n). - _Amiram Eldar_, Sep 01 2025 %p A091535 a := n -> 9^n*GAMMA(n+1/3)*GAMMA(n+2/3)*sqrt(3)/(4*Pi); %p A091535 seq(a(n), n=1..16); # _Peter Luschny_, Sep 17 2014 %t A091535 a[n_] := (3*n-1)!/(2!*3^(n-1)*(n-1)!); Array[a, 15] (* _Amiram Eldar_, Sep 01 2025 *) %Y A091535 Third column of array A091752 ((-1, 2)-Stirling2). %Y A091535 Cf. A007559, A032031, A091534. %K A091535 nonn,easy,changed %O A091535 1,2 %A A091535 _Wolfdieter Lang_, Jan 23 2004