|
|
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}]].
|
|
0
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Row sums are: {1, 2, 12, 40, 144, 480, 1600, 5248, 17152, 55808, 181248}.
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|