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%I #17 Feb 13 2016 03:56:35
%S 1,-2,5,-17,74,-394,2484,-18108,149904,-1389456,14257440,-160460640,
%T 1965444480,-26029779840,370643938560,-5646837369600,91657072281600,
%U -1579093018675200,28779361764249600,-553210247226470400
%N Difference of the first two Stirling numbers of the first kind.
%F a(n) = s(n, 1)-s(n, 2), s(n, m) = signed Stirling number of the first kind.
%F E.g.f.: (1+x)^-1 * (1-log(1+x)).
%F Conjecture: a(n) +(2*n-1)*a(n-1) +(n-1)^2*a(n-2)=0. - _R. J. Mathar_, Oct 27 2014
%t Table[StirlingS1[n+1, 1] - StirlingS1[n+1, 2], {n, 0, 20}] (* or *) Table[(-1)^n n! (1+HarmonicNumber[n]), {n, 0, 20}] (* _Jean-François Alcover_, Feb 11 2016 *)
%o (PARI) a(n) = stirling(n+1, 1, 1) - stirling(n+1, 2, 1); \\ _Michel Marcus_, Feb 11 2016
%Y Cf. A000254, A008275. Same as A000774 apart from signs.
%K easy,sign
%O 0,2
%A _Paul Barry_, Mar 05 2003