A222064 a(n) = n-th third-order hypergeometric-harmonic number.

0, 1, 8, 69, 674, 7455, 92540, 1276569, 19394870, 321982323, 5801055632, 112753640109, 2352074473226, 52419496769991, 1243115350746404, 31257697673933889, 830700701852539742, 23266435856618600859, 684997785857198880056, 21149644833172896698709

Offset: 0

Author

N. J. A. Sloane, Feb 08 2013

Keywords

• nonn

Links

• Ayhan Dil and Veli Kurt, Polynomials related to harmonic numbers and evaluation of harmonic number series I, INTEGERS, 12 (2012), #A38.

Crossrefs

Cf. A222057-A222064. Row sums of A222063.

Programs

PARI

hyp(n,alpha) = {x= y+O(y^(n+1)); gf = - log(1-x)/(1-x)^alpha; polcoeff(gf, n, y);}
a(n) = {sum(k=0, n, k!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k,3));}
\\ Michel Marcus, Feb 09 2013

Formula

a(n) = Sum_{k=0..n} A008277(n,k)*A000142(k)*H3(k) where H3(k) is defined by g.f.:- log(1-x)/(1-x)^3. - Michel Marcus, Feb 09 2013

Extensions

More terms from Michel Marcus, Feb 09 2013