|
| |
|
|
A146773
|
|
A new symmetrical polynomial form to give a triangle sequence: 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; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| Row sums are:{1, 2, 12, 40, 144, 480, 1600, 5248, 17152, 55808, 181248}.
|
|
|
FORMULA
| 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}]]; t(n,m)=coefficients(p(x,n)).
|
|
|
EXAMPLE
| {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
| Clear[p, x, n]; 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: A168644 A168620 A143683 * A202941 A166341 A113280
Adjacent sequences: A146770 A146771 A146772 * A146774 A146775 A146776
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2008
|
| |
|
|
