A157503 det(I - M) where M_jk = (j*x)^k/k!.

1, -1, -4, -21, -160, -1505, -17136, -226093, -3334528, -53031105, -864640000, -12957006821, -107329453056, 4548002439071, 409321789829120, 23780752998703875, 1257249577352658944, 65336038911885770623

Offset: 0

Author

Andrew J. Robbins, Mar 02 2009

Keywords

• easy
• sign

Comments

The n X n matrix M is a Vandermonde matrix of (x, 2x, 3x, ..., j*x, ..., n*x) scaled by factorials. The first n coefficients of x in det(I - M) are always the same.

Links

• Andrew J. Robbins, Table of n, a(n) for n = 0..50

Programs

Mathematica

A[n_] := D[Det[Table[KroneckerDelta[j,k] - (j*x)^k/k!, {j,1,n}, {k,1,n}]], {x, n}]/.x->0

Formula

E.g.f.: det(I - M) where M_jk = (j*x)^k/k!.