OFFSET
0,3
LINKS
Ayhan Dil and Veli Kurt, Polynomials related to harmonic numbers and evaluation of harmonic number series I, INTEGERS, 12 (2012), #A38.
FORMULA
a(n) = (Sum_{k=0..n} A008277(n,k) * H3(k)) * A000142(n) where H3(k) is defined by g.f.: - log(1-x)/(1-x)^3. - Michel Marcus, Feb 09 2013
PROG
(PARI)
hyp(n, alpha) = {x= y+O(y^(n+1)); gf = - log(1-x)/(1-x)^alpha; polcoeff(gf, n, y); }
a(n, alpha=3) = sum(k=0, n, n!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k, alpha));
\\ Michel Marcus, Feb 09 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, following a suggestion of N. J. A. Sloane, Feb 09 2013
STATUS
approved