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%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
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