|
Search: id:A134319
|
|
|
| A134319 |
|
A007318 * a triangle by rows: for n>0, n zeros followed by 2^n - 1. |
|
+0
2
|
|
| 1, 1, 1, 1, 2, 3, 1, 3, 9, 7, 1, 4, 18, 28, 15, 1, 5, 30, 70, 75, 31, 1, 6, 45, 140, 225, 186, 63, 1, 7, 63, 245, 525, 651, 441, 127, 1, 8, 84, 392, 1050, 1736, 1764, 1016, 255, 1, 9, 108, 588, 1890, 3906, 5292, 4572, 2295, 511, 1, 10, 135, 840, 3150, 7812, 13230, 15240
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Row sums = A083323: (1, 2, 6, 20, 66, 212, 666,...).
|
|
FORMULA
|
Binomial transform of a diagonalized infinite lower triangular matrix with (1, 1, 3, 7, 15,...) in the main diagonal and the rest zeros.
T(n,k) = |[1/(2^x)^k] 1+(1-1/2^x)^n-(1-2/2^x)^n|. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 10 2008]
|
|
EXAMPLE
|
First few rows of the triangle are:
1;
1, 1;
1, 2, 3;
1, 3, 9, 7;
1, 4, 18, 28, 15;
1, 5, 30, 70, 75, 31;
1, 6, 45, 140, 225, 186, 63;
1, 7, 63, 245, 525, 651, 441, 127;
...
|
|
MAPLE
|
x:= 'x': T:= (n, k)-> `if` (k=0, 1, abs (coeff (expand ((1-1/2^x)^n -(1-2/2^x)^n), 1/(2^x)^k))): seq (seq (T(n, k), k=0..n), n=0..12); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 10 2008]
|
|
CROSSREFS
|
Cf. A083313.
Sequence in context: A133935 A139633 A152440 this_sequence A135091 A111589 A010027
Adjacent sequences: A134316 A134317 A134318 this_sequence A134320 A134321 A134322
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 19 2007
|
|
EXTENSIONS
|
More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 10 2008
|
|
|
Search completed in 0.002 seconds
|
