|
Search: id:A093905
|
|
|
| A093905 |
|
Triangle read by rows: for 0 <= k < n, a(n, k) is the sum of the products of all subsets of {n-k, n-k+1, ..., n} with k members. |
|
+0
1
|
|
| 1, 1, 3, 1, 5, 11, 1, 7, 26, 50, 1, 9, 47, 154, 274, 1, 11, 74, 342, 1044, 1764, 1, 13, 107, 638, 2754, 8028, 13068, 1, 15, 146, 1066, 5944, 24552, 69264, 109584, 1, 17, 191, 1650, 11274, 60216, 241128, 663696, 1026576, 1, 19, 242, 2414, 19524, 127860
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
FORMULA
|
a(n, k) = [prod_{i=n-k..n} i]*[sum_{i =n-k..n} 1/i].
a(n, k) = A067176(n, n-k-1) = A105954(k+1, n-k). Row sums are given by A093344.
|
|
EXAMPLE
|
Triangle begins:
1
1 3
1 5 11
1 7 26 50
1 9 47 154 274
...
a(5, 3) = 4*3*2+5*3*2+5*4*2+5*4*3 = 154.
|
|
CROSSREFS
|
The leading diagonal is given by A000254, Stirling numbers of first kind. The next nine diagonals are A001705, A001711, A001716, A001721, A051524, A051545, A051560, A051562 and A051564, generalized Stirling numbers.
Cf. A001705, A001711, A067176, A093344, A105954.
Adjacent sequences: A093902 A093903 A093904 this_sequence A093906 A093907 A093908
Sequence in context: A122366 A103327 A065229 this_sequence A063853 A105064 A073496
|
|
KEYWORD
|
nonn,easy,tabl
|
|
AUTHOR
|
Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 24 2004
|
|
EXTENSIONS
|
Edited and extended by David Wasserman (dwasserm(AT)earthlink.net), Apr 24 2007
|
|
|
Search completed in 0.002 seconds
|
