A146773 Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

1, 1, 1, 1, 10, 1, 1, 19, 19, 1, 1, 52, 38, 52, 1, 1, 133, 106, 106, 133, 1, 1, 326, 399, 148, 399, 326, 1, 1, 775, 1301, 547, 547, 1301, 775, 1, 1, 1800, 3868, 2616, 582, 2616, 3868, 1800, 1, 1, 4105, 10788, 10324, 2686, 2686, 10324, 10788, 4105, 1, 1, 9226, 28717

Offset

0,5

Comments

Row sums are: {1, 2, 12, 40, 144, 480, 1600, 5248, 17152, 55808, 181248}.

Links

Table of n, a(n) for n=0..57.

Example

Triangle begins:
{1},
{1, 1},
{1, 10, 1},
{1, 19, 19, 1},
{1, 52, 38, 52, 1},
{1, 133, 106, 106, 133, 1},
{1, 326, 399, 148, 399, 326, 1},
{1, 775, 1301, 547, 547, 1301, 775, 1},
{1, 1800, 3868, 2616, 582, 2616, 3868, 1800, 1},
{1, 4105, 10788, 10324, 2686, 2686, 10324, 10788, 4105, 1},
{1, 9226, 28717, 35960, 15570, 2300, 15570, 35960, 28717, 9226, 1}

Mathematica

p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n)*Sum[Binomial[n-m, 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: A378544 A168620 A143683 * A202941 A166341 A113280

Adjacent sequences: A146770 A146771 A146772 * A146774 A146775 A146776

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Nov 02 2008

Status

approved