A293117 E.g.f.: exp(x^2/(x-1)).

1, 0, -2, -6, -12, 0, 240, 2520, 21840, 181440, 1481760, 11642400, 80498880, 311351040, -4739454720, -183437654400, -4300276780800, -88851284121600, -1754954007206400, -34107089784768000, -659574028252339200, -12724865943229440000, -244046146272658329600

Offset: 0

Author

Seiichi Manyama, Sep 30 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..450

Crossrefs

Column k=1 of A293119.

Cf. A052845.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, -add(
      a(n-j)*binomial(n-1, j-1)*j!, j=2..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Sep 30 2017

Mathematica

CoefficientList[Series[E^(-x^2/(1-x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2017 *)

PARI

x='x+O('x^66); Vec(serlaplace(exp(x^2/(x-1))))

Formula

D-finite with recurrence a(n) = (2*n-2)*a(n-1) - (n^2-n)*a(n-2) + (n^2-3*n+2)*a(n-3). - Robert Israel, Apr 29 2021