A103879 Square array T(n,k) read by antidiagonals: numerators of Stirling numbers of first kind with negative argument S1(-n,k), n,k>=0.

1, 1, 0, 1, -1, 0, 1, -3, 1, 0, 1, -11, 7, -1, 0, 1, -25, 85, -15, 1, 0, 1, -137, 415, -575, 31, -1, 0, 1, -49, 12019, -5845, 3661, -63, 1, 0, 1, -121, 13489, -874853, 76111, -22631, 127, -1, 0, 1, -761, 726301, -336581, 58067611, -952525, 137845, -255, 1

Offset

0,8

Links

Table of n, a(n) for n=0..53.

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

Crossrefs

Denominators are in A103880. Cf. A008969.

Sequence in context: A091480 A034374 A261318 * A322706 A051722 A357354

Adjacent sequences: A103876 A103877 A103878 * A103880 A103881 A103882

Keyword

sign,tabl,frac

Author

Ralf Stephan, Feb 20 2005

Status

approved