A080171 a(n) = n*a(n-1) - (n-1)^2*a(n-2), a(0)=1, a(1)=1.

1, 1, 1, -1, -13, -49, 31, 1981, 14329, 2177, -1138879, -12745369, -15140069, 1638512239, 25497843007, 61319246261, -4755906736399, -96548141561599, -363409501289471, 24376817341458127, 618727176794661571, 3242543776104642191, -201522721892143624609

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Feb 06 2003

Keywords

• easy
• sign

Comments

a(n) is the determinant of the n X n tridiagonal matrix M with m(i,j) = min(i,j).

Links

• R. A. Usmani, Inversion of Jacobi's Tridiagonal Matrix, Computers Math. Applic. 27 (8), (1994), 59-66.

Programs

Mathematica

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)! ]]

Formula

E.g.f.: e^(atan((-1+2z)/sqrt(3))/sqrt(3)) * e^(Pi/(6*sqrt(3))) / sqrt(1 - z + z^2).