A059422 Difference between number of even equivalence classes and odd classes of terms in a symmetric determinant of order n.

1, 1, 0, -1, -1, 3, -2, 25, -213, 1547, -13276, 129069, -1375775, 16009741, -202184274, 2753591087, -40231298023, 627731583225, -10418193719432, 183264681827863, -3406106373633009, 66695477905719251, -1372395141298236250, 29607108539572186329

Offset: 0

Author

N. J. A. Sloane, Jan 30 2001

Keywords

• sign

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 260, #12, a'_n.

Crossrefs

Cf. A002135.

Programs

Mathematica

CoefficientList[Series[E^(1/2*x-1/4*x^2)*(1+x)^(1/2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 07 2013 *)

Formula

E.g.f.: exp(1/2*t-1/4*t^2)*(1+t)^(1/2)

a(n) ~ (-1)^(n+1) * n^(n-1) / (sqrt(2)*exp(n+3/4)). - Vaclav Kotesovec, Oct 07 2013