|
Search: id:A144398
|
|
|
| A144398 |
|
Coefficients of a symmetrical polynomial set:( Pascal's triangle with central zeros) p(x,n)=If[n <= 4, Sum[Binomial[n, i]*x^i, {i, 0, n}], x^n + n*x^(n - 1) + Binomial[n, 2]*x^(n - 2) + n*x + Binomial[n, 2]*x^2 + 1]. |
|
+0
1
|
|
| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 0, 15, 6, 1, 1, 7, 21, 0, 0, 21, 7, 1, 1, 8, 28, 0, 0, 0, 28, 8, 1, 1, 9, 36, 0, 0, 0, 0, 36, 9, 1, 1, 10, 45, 0, 0, 0, 0, 0, 45, 10, 1
(list; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
Row sums are: (related to A014206)
{1, 2, 4, 8, 16, 32, 44, 58, 74, 92, 112}
|
|
FORMULA
|
p(x,n)=If[n <= 4, Sum[Binomial[n, i]*x^i, {i, 0, n}], x^n + n*x^(n - 1) + Binomial[n, 2]*x^(n - 2) + n*x + Binomial[n, 2]*x^2 + 1]; t(n,m)=coefficients(p(x,n)).
|
|
EXAMPLE
|
{1},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, 4, 6, 4, 1},
{1, 5, 10, 10, 5, 1},
{1, 6, 15, 0, 15, 6, 1},
{1, 7, 21, 0, 0, 21, 7, 1},
{1, 8, 28, 0, 0, 0, 28, 8, 1},
{1, 9, 36, 0, 0, 0, 0, 36, 9, 1},
{1, 10, 45, 0, 0, 0, 0, 0, 45, 10, 1}
|
|
MATHEMATICA
|
Clear[p, n]; p[x_, n_] = If[n <= 4, Sum[Binomial[n, i]*x^i, {i, 0, n}], x^n + n*x^(n - 1) + Binomial[n, 2]*x^(n - 2) + n*x + Binomial[n, 2]*x^2 + 1]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
|
|
CROSSREFS
|
Sequence in context: A061676 A095145 A095144 this_sequence A034932 A094495 A154926
Adjacent sequences: A144395 A144396 A144397 this_sequence A144399 A144400 A144401
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 03 2008
|
|
|
Search completed in 0.002 seconds
|
