A146765 Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 1)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

1, 1, 1, 1, 10, 1, 1, 27, 27, 1, 1, 68, 102, 68, 1, 1, 165, 330, 330, 165, 1, 1, 390, 975, 1300, 975, 390, 1, 1, 903, 2709, 4515, 4515, 2709, 903, 1, 1, 2056, 7196, 14392, 17990, 14392, 7196, 2056, 1, 1, 4617, 18468, 43092, 64638, 64638, 43092, 18468, 4617, 1, 1

Offset

0,5

Comments

Row sums are:{1, 2, 12, 56, 240, 992, 4032, 16256, 65280, 261632, 1047552}.

Links

Table of n, a(n) for n=0..55.

Example

Triangle begins:
{1},
{1, 1},
{1, 10, 1},
{1, 27, 27, 1},
{1, 68, 102, 68, 1},
{1, 165, 330, 330, 165, 1},
{1, 390, 975, 1300, 975, 390, 1},
{1, 903, 2709, 4515, 4515, 2709, 903, 1},
{1, 2056, 7196, 14392, 17990, 14392, 7196, 2056, 1},
{1, 4617, 18468, 43092, 64638, 64638, 43092, 18468, 4617, 1},
{1, 10250, 46125, 123000, 215250, 258300, 215250, 123000, 46125, 10250, 1}

Mathematica

p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 1)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]

Crossrefs

Sequence in context: A113280 A159041 A154979 * A190152 A154984 A173047

Adjacent sequences: A146762 A146763 A146764 * A146766 A146767 A146768

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Nov 02 2008

Status

approved