A132962 a(n) = n!*Sum_{d|n} (-1)^(d+1)/(d!*(n/d)!^d).

1, 0, 2, -3, 2, 5, 2, -140, 282, 819, 2, -20482, 2, 133419, 1527528, -4661085, 2, -153296429, 2, 1402482796, 36278688162, 13748957859, 2, -14081800718427, 5194672859378, 7905848380325, 2977584150505252, 12956452725792600, 2, -1314647260913859151

Offset: 1

Author

Vladeta Jovovic, Sep 06 2007

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A038041, A132958, A132959, A132960, A132961, A132963.

Programs

Mathematica

Rest[ Range[0, 30]! CoefficientList[ Series[ Sum[1 - Exp[ -x^k/k! ], {k, 30}], {x, 0, 30}], x]] (* Robert G. Wilson v, Sep 13 2007 *)

PARI

a(n) = n!*sumdiv(n, d, (-1)^(d+1)/(d!*(n/d)!^d)); \\ Michel Marcus, Sep 29 2017

Formula

E.g.f.: Sum_{k>0}(1-exp(-x^k/k!)).

Extensions

More terms from Robert G. Wilson v, Sep 13 2007