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.

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

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%I A222062 #14 Apr 25 2019 04:45:20
%S A222062 0,1,6,42,346,3310,36194,446054,6122442,92668302,1533812722,
%T A222062 27565147126,534621745178,11131104732254,247646911102530,
%U A222062 5863652049020358,147225092025474154,3907328980930705966,109297865960259305618,3214017757399205062550,99121172016580291190970
%N A222062 a(n) = n-th second-order hypergeometric-harmonic number.
%H A222062 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 A222062 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
%o A222062 (PARI)
%o A222062 hyp(n,alpha) = {x= y+O(y^(n+1)); gf = - log(1-x)/(1-x)^alpha; polcoeff(gf, n, y);}
%o A222062 a(n) = {sum(k=0, n, k!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k,2));}
%o A222062 \\ _Michel Marcus_, Feb 09 2013
%Y A222062 Cf. A222057-A222064. Row sums of A222061.
%K A222062 nonn
%O A222062 0,3
%A A222062 _N. J. A. Sloane_, Feb 08 2013
%E A222062 More terms from _Michel Marcus_, Feb 09 2013