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 A222064 a(n) = n-th third-order hypergeometric-harmonic number. 4
 0, 1, 8, 69, 674, 7455, 92540, 1276569, 19394870, 321982323, 5801055632, 112753640109, 2352074473226, 52419496769991, 1243115350746404, 31257697673933889, 830700701852539742, 23266435856618600859, 684997785857198880056, 21149644833172896698709 (list; graph; refs; listen; history; text; internal format)
 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)*A000142(k)*H3(k) 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) = {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 CROSSREFS Cf. A222057-A222064. Row sums of A222063. Sequence in context: A214344 A228421 A152109 * A317096 A327606 A226597 Adjacent sequences:  A222061 A222062 A222063 * A222065 A222066 A222067 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 08 2013 EXTENSIONS More terms from Michel Marcus, Feb 09 2013 STATUS approved

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Last modified June 4 04:39 EDT 2020. Contains 334815 sequences. (Running on oeis4.)