%I A117742
%S A117742 0,0,0,1,1,1,1,2,3,4,1,4,9,16,25,1,8,27,64,125,216,2,17,82,257,626,1297,
%T A117742 2402,3,36,249,1032,3135,7788,16821,32784,4,76,756,4144,15700,46764,
%U A117742 117796,262336,531684,5,160,2295,16640,78625,280800,824915,2099200
%N A117742 Triangular expansion of A003269 using the rational polynomial:p[x_] = 
               x/(1 - m*x - x^4);.
%F A117742 a(n,m)= A003296[n,m]
%e A117742 0
%e A117742 0, 0
%e A117742 1, 1, 1
%e A117742 1, 2, 3, 4
%e A117742 1, 4, 9, 16, 25
%e A117742 1, 8, 27, 64, 125, 216
%e A117742 2, 17, 82, 257, 626, 1297, 2402
%e A117742 3, 36, 249, 1032, 3135, 7788, 16821, 32784
%t A117742 (* define the polynomial*) p[x_] = x/(1 - m*x - x^4); (* Taylor derivative 
               expansion of the polynomial*) a = Table[Flatten[{{p[0]}, Table[Coefficient[Series[p[x], 
               {x, 0, 30}], x^n], {n, 1, 10}]}], {m, 1, 10}] (*antidiagonal expansion 
               to give triangular function*) b = Join[{{ 0}}, Delete[Table[Table[a[[n]][[m]], 
               {n, 1, m + 1}], {m, 0, 9}], 1]] Flatten[b]
%Y A117742 Cf. A003269.
%Y A117742 Sequence in context: A003324 A110630 A129717 this_sequence A117716 A097150 
               A087165
%Y A117742 Adjacent sequences: A117739 A117740 A117741 this_sequence A117743 A117744 
               A117745
%K A117742 nonn,uned,probation
%O A117742 0,8
%A A117742 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 14 2006