A153312 - OEIS

%I #2 Mar 30 2012 17:34:28

%S 2,3,3,2,14,2,2,25,25,2,2,36,86,36,2,2,47,140,140,47,2,2,76,241,334,

%T 241,76,2,2,159,479,737,737,479,159,2,2,404,1124,1702,1960,1702,1124,

%U 404,2,2,1135,2986,4284,5120,5120,4284,2986,1135,2,2,3324,8495,11644,13778

%N Coefficient triangle sequence of a polynomial recursion: p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 3)*Sum[x^i, {i, 1, n - 2}]); Row sums approximate 2*3^n.

%C Row sums:

%C {2, 6, 18, 54, 162, 378, 972, 2754, 8424, 27054, 89100,...}.

%F p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 3)*Sum[x^i, {i, 1, n - 2}]).

%e {2},

%e {3, 3},

%e {2, 14, 2},

%e {2, 25, 25, 2},

%e {2, 36, 77, 45, 2},

%e {2, 65, 167, 176, 74, 2},

%e {2, 148, 313, 424, 412, 157, 2},

%e {2, 393, 704, 980, 1079, 812, 402, 2},

%e {2, 1124, 1826, 1684, 2788, 2620, 1943, 1133, 2},

%e {2, 3313, 5137, 3510, 6659, 7595, 4563, 5263, 3322, 2},

%e {2, 9876, 15011, 8647, 10169, 20815, 18719, 9826, 15146, 9885, 2}

%t Clear[p, n, m, x];

%t p[x, 3] = 2*x^3 + 25*x^2 + 25*x + 2;

%t p[x, 4] = 2*x^4 + 36*x^3 + 86*x^2 + 36*x + 2;

%t p[x_, n_] := p[x, n] = (x + 1)*(p[x, n - 1] + 3^(n - 3)*Sum[x^i, {i, 1, n - 2}]);

%t Table[ExpandAll[p[x, n]], {n, 0, 10}];

%t Table[CoefficientList[p[x, n], x], {n, 0, 10}];

%t Flatten[%]

%K nonn,uned,tabl

%O 0,1

%A _Roger L. Bagula_, Dec 23 2008