cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A222064 #24 Apr 25 2019 04:45:40
%S A222064 0,1,8,69,674,7455,92540,1276569,19394870,321982323,5801055632,
%T A222064 112753640109,2352074473226,52419496769991,1243115350746404,
%U A222064 31257697673933889,830700701852539742,23266435856618600859,684997785857198880056,21149644833172896698709
%N A222064 a(n) = n-th third-order hypergeometric-harmonic number.
%H A222064 Ayhan Dil and Veli Kurt, <a href="https://www.emis.de/journals/INTEGERS/papers/m38/m38.Abstract.html">Polynomials related to harmonic numbers and evaluation of harmonic number series I</a>, INTEGERS, 12 (2012), #A38.
%F A222064 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
%o A222064 (PARI)
%o A222064 hyp(n,alpha) = {x= y+O(y^(n+1)); gf = - log(1-x)/(1-x)^alpha; polcoeff(gf, n, y);}
%o A222064 a(n) = {sum(k=0, n, k!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k,3));}
%o A222064 \\ _Michel Marcus_, Feb 09 2013
%Y A222064 Cf. A222057-A222064. Row sums of A222063.
%K A222064 nonn
%O A222064 0,3
%A A222064 _N. J. A. Sloane_, Feb 08 2013
%E A222064 More terms from _Michel Marcus_, Feb 09 2013