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, 1, 1, 2, 1, 1, 6, 4, 1, 1, 24, 36, 8, 1, 1, 120, 288, 216, 16, 1, 1, 720, 7200, 3456, 1296, 32, 1, 1, 5040, 14400, 432000, 41472, 7776, 64, 1, 1, 40320, 235200, 2592000, 25920000, 497664, 46656, 128, 1, 1, 362880, 11289600, 889056000, 51840000

Offset

0,4

Links

Table of n, a(n) for n=0..48.

D. Loeb, Generalization of the Stirling numbers of first kind

Formula

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

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

Example

1, 0, 0, 0, 0, 0,
1, -1, 1, -1, 1, -1,
1/2, -3/4, 7/8, -15/16, 31/32, -63/64,
1/6, -11/36, 85/216, -575/1296, 3661/7776, -22631/46656,
1/24,-25/288,415/3456,-5845/41472,76111/497664,-952525/5971968,

Prog

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

Crossrefs

Numerators are in A103879. Cf. A008969.

Sequence in context: A139622 A257895 A186023 * A135899 A327816 A047920

Adjacent sequences: A103877 A103878 A103879 * A103881 A103882 A103883

Keyword

nonn,tabl,frac

Author

Ralf Stephan, Feb 20 2005

Status

approved