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Generalized Stirling numbers of the first kind.
2

%I #8 Nov 23 2020 17:07:00

%S 1,0,5,-5,74,-154,2484,-8028,149904,-663696,14257440,-80627040,

%T 1965444480,-13575738240,370643938560,-3031488633600,91657072281600,

%U -867718162483200,28779361764249600,-309920046408806400,11185850044938240000,-135153868608460800000

%N Generalized Stirling numbers of the first kind.

%H Robert Israel, <a href="/A081049/b081049.txt">Table of n, a(n) for n = 0..449</a>

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

%F E.g.f.: 1/(1-x) - log(1+x)/(1+x). - _Robert Israel_, Nov 23 2020

%p E:= 1/(1-x) - ln(1+x)/(1+x):

%p S:= series(E,x,51):

%p seq(coeff(S,x,n)*n!, n=0..50); # _Robert Israel_, Nov 23 2020

%Y Cf. A000774, A081050, A008275.

%K easy,sign

%O 0,3

%A _Paul Barry_, Mar 05 2003