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%I #16 Sep 10 2023 09:46:54
%S 1,1,1,-1,-13,-49,31,1981,14329,2177,-1138879,-12745369,-15140069,
%T 1638512239,25497843007,61319246261,-4755906736399,-96548141561599,
%U -363409501289471,24376817341458127,618727176794661571,3242543776104642191,-201522721892143624609
%N a(n) = n*a(n-1) - (n-1)^2*a(n-2), a(0)=1, a(1)=1.
%C a(n) is the determinant of the n X n tridiagonal matrix M with m(i,j) = min(i,j).
%H R. A. Usmani, <a href="https://doi.org/10.1016/0898-1221(94)90066-3">Inversion of Jacobi's Tridiagonal Matrix</a>, Computers Math. Applic. 27 (8), (1994), 59-66.
%F E.g.f.: e^(atan((-1+2z)/sqrt(3))/sqrt(3)) * e^(Pi/(6*sqrt(3))) / sqrt(1 - z + z^2).
%t c=CoefficientList[Series[Exp[ArcTan[(-1+2z)/Sqrt[3]]/Sqrt[3]]*Exp[Pi/(6*Sqrt[3])]/Sqrt[1 - z + z^2], {z, 0, 25}], z]; For[n=0, n<26, n++; Print[c[[n]]*(n-1)! ]]
%K easy,sign
%O 0,5
%A Mario Catalani (mario.catalani(AT)unito.it), Feb 06 2003