|
Search: id:A080416
|
|
|
| A080416 |
|
Stirling-like number triangle defined by paired decomposition of C(n+3,3) = A000292. |
|
+0
2
|
|
| 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; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
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.
|
|
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.
Adjacent sequences: A080413 A080414 A080415 this_sequence A080417 A080418 A080419
Sequence in context: A008292 A101919 A055106 this_sequence A099759 A072590 A111636
|
|
KEYWORD
|
easy,nonn,tabl
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Feb 17 2003
|
|
|
Search completed in 0.002 seconds
|
