A222062 a(n) = n-th second-order hypergeometric-harmonic number.

0, 1, 6, 42, 346, 3310, 36194, 446054, 6122442, 92668302, 1533812722, 27565147126, 534621745178, 11131104732254, 247646911102530, 5863652049020358, 147225092025474154, 3907328980930705966, 109297865960259305618, 3214017757399205062550, 99121172016580291190970

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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)*A000142(k)*H2(k) where H2(k) is defined by g.f.: - log(1-x)/(1-x)^2. - 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) = {sum(k=0, n, k!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k, 2)); }
\\ Michel Marcus, Feb 09 2013

Crossrefs

Cf. A222057-A222064. Row sums of A222061.

Sequence in context: A132804 A232473 A300693 * A074017 A135887 A218817

Adjacent sequences: A222059 A222060 A222061 * A222063 A222064 A222065

Keyword

nonn

Author

N. J. A. Sloane, Feb 08 2013

Extensions

More terms from Michel Marcus, Feb 09 2013

Status

approved