A171146 The sequence of coefficients of a polynomial recursion: p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + (2*n - 1)*x + 1)^Floor[n/2]] ( correction).

1, 1, 1, 1, 5, 1, 1, 6, 6, 1, 1, 18, 83, 18, 1, 1, 19, 101, 101, 19, 1, 1, 39, 510, 2275, 510, 39, 1, 1, 40, 549, 2785, 2785, 549, 40, 1, 1, 68, 1738, 19856, 86995, 19856, 1738, 68, 1, 1, 69, 1806, 21594, 106851, 106851, 21594, 1806, 69, 1, 1, 105, 4415, 93030, 985645

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Dec 04 2009

Keywords

• nonn
• tabl

Comments

Row sums are:

{1, 2, 7, 14, 121, 242, 3375, 6750, 130321, 260642, 6436343, 12872686...}.

Examples

			{1},
{1, 1},
{1, 5, 1},
{1, 6, 6, 1},
{1, 18, 83, 18, 1},
{1, 19, 101, 101, 19, 1},
{1, 39, 510, 2275, 510, 39, 1},
{1, 40, 549, 2785, 2785, 549, 40, 1},
{1, 68, 1738, 19856, 86995, 19856, 1738, 68, 1},
{1, 69, 1806, 21594, 106851, 106851, 21594, 1806, 69, 1},
{1, 105, 4415, 93030, 985645, 4269951, 985645, 93030, 4415, 105, 1},
{1, 106, 4520, 97445, 1078675, 5255596, 5255596, 1078675, 97445, 4520, 106, 1}
		

Crossrefs

Cf. A051159 , A169623, A007318, A171142, A171143

Programs

Mathematica

Clear[p, n, x, a]
p[x, 1] := 1;
p[x_, n_] := p[x, n] = If[Mod[n, 2] == 0, (x + 1)*p[x, n - 1], (x^2 + (2*n - 1)*x + 1)^Floor[n/2]];
a = Table[CoefficientList[p[x, n], x], {n, 1, 12}];
Flatten[a]

Formula

p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + (2*n - 1)*x + 1)^Floor[n/2]]