|
Search: id:A156732
|
|
|
| A156732 |
|
A triangular sequence: t(n,m)=((n + 1 - 2*m)^2/(n + 1 - m))*Binomial[n, m]. |
|
+0
1
|
|
| 0, 1, 1, 4, 0, 4, 9, 2, 2, 9, 16, 10, 0, 10, 16, 25, 27, 5, 5, 27, 25, 36, 56, 28, 0, 28, 56, 36, 49, 100, 84, 14, 14, 84, 100, 49, 64, 162, 192, 84, 0, 84, 192, 162, 64, 81, 245, 375, 270, 42, 42, 270, 375, 245, 81
(list; table; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Row sums are:
{0, 2, 10, 36, 108, 290, 726, 1736, 4024, 9126, 20370,...}.
From the Riordan Identity:
2^n=Table[Sum[(( n + 1 - 2*m)^2/(n + 1 - m))*Binomial[n, m], {m, 0, Floor[n/2]}], {n, 0, 10}].
Because of the central zeros,
I call it an hollow sequence.
|
|
REFERENCES
|
J. Riordan, Combinatorial Identities, Wiley, 1968
|
|
FORMULA
|
t(n,m)=((n + 1 - 2*m)^2/(n + 1 - m))*Binomial[n, m].
|
|
EXAMPLE
|
{0},
{1, 1},
{4, 0, 4},
{9, 2, 2, 9},
{16, 10, 0, 10, 16},
{25, 27, 5, 5, 27, 25},
{36, 56, 28, 0, 28, 56, 36},
{49, 100, 84, 14, 14, 84, 100, 49},
{64, 162, 192, 84, 0, 84, 192, 162, 64},
{81, 245, 375, 270, 42, 42, 270, 375, 245, 81}
|
|
MATHEMATICA
|
Table[Table[((n + 1 - 2* m)^2/(n + 1 - m))*Binomial[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]
|
|
CROSSREFS
|
Sequence in context: A055951 A165032 A088374 this_sequence A101980 A058536 A154854
Adjacent sequences: A156729 A156730 A156731 this_sequence A156733 A156734 A156735
|
|
KEYWORD
|
nonn,tabl,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 14 2009
|
|
|
Search completed in 0.002 seconds
|
