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A222063 Triangle read by rows: coefficients of third-order hypergeometric-harmonic polynomials.

%I A222063 #13 Apr 25 2019 04:45:24
%S A222063 0,0,1,0,1,7,0,1,21,47,0,1,49,282,342,0,1,105,1175,3420,2754,0,1,217,
%T A222063 4230,22230,41310,24552,0,1,441,14147,119700,385560,515592,241128,0,1,
%U A222063 889,45402,581742,2891700,6530832,6751584,2592720,0,1,1785,142175,2657340
%N A222063 Triangle read by rows: coefficients of third-order hypergeometric-harmonic polynomials.
%H A222063 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 A222063 T(n,k) = 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
%e A222063 Triangle begins:
%e A222063 0
%e A222063 0 1
%e A222063 0 1 7
%e A222063 0 1 21 47
%e A222063 0 1 49 282 342
%e A222063 0 1 105 1175 3420 2754
%e A222063 ....
%o A222063 (PARI)
%o A222063 hyp(n,alpha) = {x= y+O(y^(n+1)); gf = - log(1-x)/(1-x)^alpha; polcoeff(gf, n, y);}
%o A222063 t(n, k) = {k!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k,3)};
%o A222063 \\ _Michel Marcus_, Feb 09 2013
%Y A222063 Cf. A222057-A222064. Row sums give A222064.
%K A222063 nonn,tabl
%O A222063 0,6
%A A222063 _N. J. A. Sloane_, Feb 08 2013
%E A222063 More terms from _Michel Marcus_, Feb 09 2013