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%I #2 Mar 30 2012 17:34:28
%S 2,5,5,2,46,2,2,123,123,2,2,250,746,250,2,2,502,2496,2496,502,2,2,
%T 1754,4248,11242,10498,1754,2,2,8006,12252,46740,52990,18502,8006,2,2,
%U 39258,51508,58992,255980,227742,57758,39258,2,2,195510,247016,110500,1096222
%N Triangle of coefficients from a polynomial recursion with row sum near =2*5^n: p(x,n)=(x + 1)*(p(x, n - 1) + 2*5^(n - 2)*(x + 5*x^Floor[n/2] + x^(n - 2))).
%C Row sums are: {2, 10, 50, 250, 1250, 6000, 29500, 146500, 730500, 3648500, 18234500,...}.
%C The first five rows are computed by hand to row sum 2*5^n.
%C The recursion is an approximation form.
%F p(x,n)=(x + 1)*(p(x, n - 1) + 2*5^(n - 2)*(x + 5*x^Floor[n/2] + x^(n - 2))).
%e {2},
%e {5, 5},
%e {2, 46, 2},
%e {2, 123, 123, 2},
%e {2, 250, 746, 250, 2},
%e {2, 502, 2496, 2496, 502, 2},
%e {2, 1754, 4248, 11242, 10498, 1754, 2},
%e {2, 8006, 12252, 46740, 52990, 18502, 8006, 2},
%e {2, 39258, 51508, 58992, 255980, 227742, 57758, 39258, 2},
%e {2, 195510, 247016, 110500, 1096222, 1264972, 285500, 253266, 195510, 2},
%e {2, 976762, 1223776, 357516, 1206722, 6267444, 5456722, 538766, 1230026, 976762, 2}
%t Clear[p, n, m, x]'
%t p[x, 0] = 2; p[x, 1] = 5*x + 5;
%t p[x, 2] = 2*x^2 + 46*x + 2; p[x, 3] = 2*x^3 + 123*x^2 + 123*x + 2;
%t p[x, 4] = 2 + 250*x + 746*x^2 + 250*x^3 + 2*x^4;
%t p[x_, n_] := p[x, n] = (x + 1)*(p[x, n - 1] + 2*5^(n - 2)*(x + 5*x^Floor[n/ 2] + x^(n - 2)));
%t Table[ExpandAll[p[x, n]], {n, 0, 10}];
%t b = Table[CoefficientList[p[x, n], x], {n, 0, 10}];
%t Flatten[%]
%K nonn,uned,tabl
%O 0,1
%A _Roger L. Bagula_, Dec 24 2008
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