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%I #19 Apr 28 2016 11:36:55
%S 1,1,2,1,0,0,21,132,294,252,21,-56,0,8,0,35,450,2293,5700,6405,770,
%T -3661,-240,2320,40,-672,0,0,9555,207480,1889316,9216312,25051026,
%U 33229560,3678948,-35339304,-2666157,51171120,2178176,-49878192,-792064,24460800,4160,-3714816,0
%N Triangle of numerators of coefficients of the polynomial Q^(3)_m(n) defined by the recursion Q^(3)_0(n)=1; for m>=1, Q^(3)_m(n) = Sum_{i=1...n} i^3*Q^(3)_(m-1)(i).
%C For m>=0, the denominator for all 4*m+1 terms of the m-th row is A202368(m+1).
%C See comment to A175669.
%F Q^(3)_n(1)=1.
%e The sequence of polynomials begins
%e Q^(3)_0=1,
%e Q^(3)_1=(x^4+2*x^3+x^2)/4,
%e Q^(3)_2=(21*x^8+132*x^7+294*x^6+252*x^5+21*x^4-56*x^3+8*x)/672,
%e Q^(3)_3=(35*x^12+450*x^11+2293*x^10+5700*x^9+6405*x^8+770*x^7-3661*x^6-240*x^5+2320*x^4+40x^3-672*x^2)/13440.
%Y Cf. A202339, A053657, A202367, A202368, A202369, A175699.
%K sign,tabf
%O 0,3
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Dec 23 2011
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