A153310 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.

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, 133, 31, 2, 2, 1113, 1703, 908, 449, 164, 33, 2, 2, 3302, 5003, 2611, 1357, 613, 197, 35, 2, 2, 9865, 14866, 7614, 3968, 1970, 810, 232, 37, 2, 2, 29550, 44414, 22480, 11582

Offset: 0

Author

Roger L. Bagula, Dec 23 2008

Keywords

• nonn
• uned
• tabl

Comments

Row sums:

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

Examples

			{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, 133, 31, 2},
{2, 1113, 1703, 908, 449, 164, 33, 2},
{2, 3302, 5003, 2611, 1357, 613, 197, 35, 2},
{2, 9865, 14866, 7614, 3968, 1970, 810, 232, 37, 2},
{2, 29550, 44414, 22480, 11582, 5938, 2780, 1042, 269, 39, 2}
		

Crossrefs

A025192

Programs

Mathematica

Clear[p, n, m, x];
p[x, 0] = 2; p[x, 1] = 3*x + 3; p[x, 2] = 2*x^2 + 14*x + 2;
p[x_, n_] := p[x, n] = (x + 1)*(p[x, n - 1] + 3^(n - 1)*x);
Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[%]

Formula

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