|
| |
|
|
A080416
|
|
Stirling-like number triangle defined by paired decomposition of C(n+3,3) = A000292.
|
|
1
| |
|
|
1, 1, 1, 1, 4, 1, 1, 12, 10, 1, 1, 32, 67, 20, 1, 1, 80, 376, 252, 35, 1, 1, 192, 1909, 2560, 742, 56, 1, 1, 448, 9094, 22928, 12346, 1848, 84, 1, 1, 1024, 41479, 189120, 177599, 46912, 4074, 120, 1, 1, 2304, 183412, 1472704, 2318149
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| Note that the Stirling numbers of the second kind are generated in a similar fashion by decomposing the triangular numbers C(n+2,2) as {1}, {1,2}, {1,2,3} .... The defining sequence A000292 appears as the sub-diagonal when the triangle is arranged in lower-triangular form. The second column is A001787.
Gives the number of ways to construct pairs of k-block partitions from 1 to n such that the sum of the minima of the i-th block of the first partition and the (k-i+1)th block of the second partition is n+1. - Ken Joffaniel Gonzales (kenjo_kenjo(AT)yahoo.com), Jun 13 2010
|
|
|
FORMULA
| Columns are generated as follows : Display C(n+3, 3) as row sums of the triangle A080251, or {1}, {2, 2}, {3, 3, 4}, {4, 4, 6, 6}, {5, 5, 8, 8, 9}, ... The columns are then generated by 1/(1-x), 1/(1-2x)^2, 1/(1-3x)^2(1-4x)), 1/((1-4x)^2(1-6x)^2)) etc
|
|
|
EXAMPLE
| Rows are {1}, {1,1}, {1,4,1}, {1,12,10,1}, {1,32,67,20,1},...
|
|
|
CROSSREFS
| Cf. A080251, A000292, A008277, A001787.
Sequence in context: A101919 A055106 A154372 * A168619 A099759 A072590
Adjacent sequences: A080413 A080414 A080415 * A080417 A080418 A080419
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 17 2003
|
| |
|
|
