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

0,3

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

Formula

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

Mathematica

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

Crossrefs

Sequence in context: A357424 A166901 A060072 * A144010 A366184 A179496

Adjacent sequences: A157500 A157501 A157502 * A157504 A157505 A157506

Keyword

easy,sign

Author

Andrew J. Robbins, Mar 02 2009

Status

approved