OFFSET
0,6
LINKS
Ayhan Dil and Veli Kurt, Polynomials related to harmonic numbers and evaluation of harmonic number series I, INTEGERS, 12 (2012), #A38.
FORMULA
T(n,k) = A008277(n,k)*A000142(k)*H2(k) where H2(k) is defined by g.f.:- log(1-x)/(1-x)^2. - Michel Marcus, Feb 09 2013
EXAMPLE
Triangle begins:
0
0 1
0 1 5
0 1 15 26
0 1 35 156 154
0 1 75 650 1540 1044
....
MATHEMATICA
H2[k_] := (k+1) (HarmonicNumber[k+1] - 1);
T[n_, k_] := StirlingS2[n, k] k! H2[k];
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 01 2018 *)
PROG
(PARI)
hyp(n, alpha) = {x= y+O(y^(n+1)); gf = - log(1-x)/(1-x)^alpha; polcoeff(gf, n, y); }
t(n, k) = {k!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k, 2)};
\\ Michel Marcus, Feb 09 2013
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Feb 08 2013
EXTENSIONS
More terms from Michel Marcus, Feb 09 2013
STATUS
approved