A081049 Generalized Stirling numbers of the first kind.

1, 0, 5, -5, 74, -154, 2484, -8028, 149904, -663696, 14257440, -80627040, 1965444480, -13575738240, 370643938560, -3031488633600, 91657072281600, -867718162483200, 28779361764249600, -309920046408806400, 11185850044938240000, -135153868608460800000

Offset: 0

Author

Paul Barry, Mar 05 2003

Keywords

• easy
• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A000774, A081050, A008275.

Programs

Maple

E:= 1/(1-x) - ln(1+x)/(1+x):
S:= series(E,x,51):
seq(coeff(S,x,n)*n!, n=0..50); # Robert Israel, Nov 23 2020

Formula

a(n) = n!*(1 + Sum {k=1..n, (-1)^n*1/k}).

E.g.f.: 1/(1-x) - log(1+x)/(1+x). - Robert Israel, Nov 23 2020