|
| |
|
|
A059268
|
|
Concatenate subsequences [2^0, 2^1, ..., 2^n] for n = 0, 1, 2, ...
|
|
17
| |
|
|
1, 1, 2, 1, 2, 4, 1, 2, 4, 8, 1, 2, 4, 8, 16, 1, 2, 4, 8, 16, 32, 1, 2, 4, 8, 16, 32, 64, 1, 2, 4, 8, 16, 32, 64, 128, 1, 2, 4, 8, 16, 32, 64, 128, 256, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 1, 2, 4, 8, 16, 32, 64
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Triangular array T(n,k) read by rows, where T(n,k) = i!*j! times coefficient of x^n*y^k in exp(x+2y).
a(n) = A018900(n+1) - A140513(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 24 2009]
T(n,k) = A173786(n-1,k-1) - A173787(n-1,k-1), 0<k<=n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 28 2010]
T(n,k) is the number of subsets of {0,1,...,n} whose largest element is k. To see this, let A be any subset of the 2^k subsets of {0,1,...,k-1}. Then there are 2^k subsets of the form (A U {k}). See example below. [From Dennis P. Walsh, Nov 27 2011]
|
|
|
LINKS
| J. L. Arregui, Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles.
|
|
|
FORMULA
| E.g.f.: exp(x+2*y) (T coordinates).
T(n,k) = 2^k. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 29 2010]
|
|
|
EXAMPLE
| T(4,3)=8 since there are 8 subsets of {0,1,2,3,4} whose largest element is 3, namely, {3}, {0,3}, {1,3}, {2,3}, {0,1,3}, {0,2,3}, {1,2,3}, and {0,1,2,3}.
|
|
|
MAPLE
| seq(seq(2^k, k=0..n), n=0..10);
|
|
|
CROSSREFS
| A140531. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 24 2009]
Sequence in context: A168266 A059250 A131074 * A123937 A138882 A074634
Adjacent sequences: A059265 A059266 A059267 * A059269 A059270 A059271
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 23 2001
|
|
|
EXTENSIONS
| Formular corrected by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 23 2010
|
| |
|
|
