|
Search: id:A146769
|
|
|
| A146769 |
|
A new symmetrical polynomial form to give a triangle sequence: p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 4)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]. |
|
+0
1
|
|
| 1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 12, 18, 12, 1, 1, 25, 50, 50, 25, 1, 1, 54, 135, 180, 135, 54, 1, 1, 119, 357, 595, 595, 357, 119, 1, 1, 264, 924, 1848, 2310, 1848, 924, 264, 1, 1, 585, 2340, 5460, 8190, 8190, 5460, 2340, 585, 1, 1, 1290, 5805, 15480, 27090, 32508
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Row sums are:{1, 2, 5, 14, 44, 152, 560, 2144, 8384, 33152, 131840}.
|
|
FORMULA
|
p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 4)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)).
|
|
EXAMPLE
|
{1}, {1, 1}, {1, 3, 1}, {1, 6, 6, 1}, {1, 12, 18, 12, 1}, {1, 25, 50, 50, 25, 1}, {1, 54, 135, 180, 135, 54, 1}, {1, 119, 357, 595, 595, 357, 119, 1}, {1, 264, 924, 1848, 2310, 1848, 924, 264, 1}, {1, 585, 2340, 5460, 8190, 8190, 5460, 2340, 585, 1}, {1, 1290, 5805, 15480, 27090, 32508, 27090, 15480, 5805, 1290, 1}
|
|
MATHEMATICA
|
Clear[p, x, n]; p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 4)*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: A098568 A131235 A157243 this_sequence A143362 A133713 A008278
Adjacent sequences: A146766 A146767 A146768 this_sequence A146770 A146771 A146772
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2008
|
|
|
Search completed in 0.002 seconds
|
