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A103880 Square array T(n,k) read by antidiagonals: denominators of Stirling numbers of first kind with negative argument S1(-n,k), n,k>=0. 1

%I

%S 1,1,1,2,1,1,6,4,1,1,24,36,8,1,1,120,288,216,16,1,1,720,7200,3456,

%T 1296,32,1,1,5040,14400,432000,41472,7776,64,1,1,40320,235200,2592000,

%U 25920000,497664,46656,128,1,1,362880,11289600,889056000,51840000

%N Square array T(n,k) read by antidiagonals: denominators of Stirling numbers of first kind with negative argument S1(-n,k), n,k>=0.

%H D. Loeb, <a href="http://arXiv.org/abs/math.CO/9502217">Generalization of the Stirling numbers of first kind</a>

%F T(n, k) = (-1)^(k+1) * Sum[i=1..n, C(n, i)*(-1)^i*i^(-k) ].

%F G.f. of n-th row: 1/n! * 1/Prod[i=1..n, 1+x/i ].

%e 1, 0, 0, 0, 0, 0,

%e 1, -1, 1, -1, 1, -1,

%e 1/2, -3/4, 7/8, -15/16, 31/32, -63/64,

%e 1/6, -11/36, 85/216, -575/1296, 3661/7776, -22631/46656,

%e 1/24,-25/288,415/3456,-5845/41472,76111/497664,-952525/5971968,

%o (PARI) T(n,k)=denominator(1/n!*polcoeff(Ser(1/prod(i=1,n,1+x/i)),k))

%Y Numerators are in A103879. Cf. A008969.

%K nonn,tabl,frac

%O 0,4

%A _Ralf Stephan_, Feb 20 2005

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)