A153310 - OEIS

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

%S 2,3,3,2,14,2,2,25,25,2,2,54,77,27,2,2,137,212,104,29,2,2,382,592,316,

%T 133,31,2,2,1113,1703,908,449,164,33,2,2,3302,5003,2611,1357,613,197,

%U 35,2,2,9865,14866,7614,3968,1970,810,232,37,2,2,29550,44414,22480,11582

%N Coefficient triangle sequence of a polynomial recursion: p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 1)*x); Row sums are 2*3^n.

%C Row sums:

%C {2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098,...}.

%F p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 1)*x).

%e {2},

%e {3, 3},

%e {2, 14, 2},

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

%e {2, 54, 77, 27, 2},

%e {2, 137, 212, 104, 29, 2},

%e {2, 382, 592, 316, 133, 31, 2},

%e {2, 1113, 1703, 908, 449, 164, 33, 2},

%e {2, 3302, 5003, 2611, 1357, 613, 197, 35, 2},

%e {2, 9865, 14866, 7614, 3968, 1970, 810, 232, 37, 2},

%e {2, 29550, 44414, 22480, 11582, 5938, 2780, 1042, 269, 39, 2}

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

%t p[x, 0] = 2; p[x, 1] = 3*x + 3; p[x, 2] = 2*x^2 + 14*x + 2;

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

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

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

%t Flatten[%]

%Y A025192

%K nonn,uned,tabl

%O 0,1

%A _Roger L. Bagula_, Dec 23 2008