A222062 - OEIS

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

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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)); }