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A202749 Triangle of numerators of coefficients of the polynomial Q^(4)m(n)</span> defined by the recursion <span class="maths">Q^(4)_0(n)=1;</span> for <span class="maths">m>=1,Q^(4)_m(n)=sum{i=1,...,n}i^4*Q^(4)(m-1)(i). For m>=0, the denominator for all 5*m+1 terms of the m-th row is A202369(m+1).

%I A202749 #20 Jun 02 2025 07:27:11
%S A202749 1,6,15,10,0,-1,0,36,280,795,900,88,-450,-20,200,1,-30,0,19656,311220,
%T A202749 1991430,6354075,9367722,1283100,-10854935,-1064700,16237338,615615,
%U A202749 -16336320,-136500,8189909,8190,-1243800,0
%N A202749 Triangle of numerators of coefficients of the polynomial Q^(4)_m(n) defined by the recursion Q^(4)_0(n)=1; for m>=1,Q^(4)_m(n)=sum{i=1,...,n}i^4*Q^(4)_(m-1)(i). For m>=0, the denominator for all 5*m+1 terms of the m-th row is A202369(m+1).
%C A202749 See comment in A175669.
%F A202749 Q^(4)_n(1)=1.
%e A202749 The sequence of polynomials begins
%e A202749 Q^(3)_0=1,
%e A202749 Q^(3)_1=(6*x^5+15*x^4+10*x^3-x)/30,
%e A202749 Q^(3)_2=(36*x^10+280*x^9+795*x^8+900*x^7+88*x^6-450*x^5-20*x^4+200*x^3+x^2-30*x)/1800.
%Y A202749 Cf. A202339, A053657, A202367, A202368, A202369, A175699, A202717
%K A202749 sign,tabf
%O A202749 0,2
%A A202749 _Vladimir Shevelev_ and _Peter J. C. Moses_, Dec 23 2011