|
Search: id:A090217
|
|
|
| A090217 |
|
A generalization of triangle A0715951 (Legendre-Stirling). |
|
+0
4
|
|
| 1, 120, 1, 14400, 840, 1, 1728000, 619200, 3360, 1, 207360000, 447552000, 9086400, 10080, 1, 24883200000, 322444800000, 23345280000, 76824000, 25200, 1, 2985984000000, 232185139200000, 59152550400000, 539602560000, 457848000
(list; table; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
This is the fourth member of the family A071951 (Legendre-Stirling,(2,2) case), A089504((3,3)-case), A090215 ((4,4)-case).
This triangle underlies the array entry A090216 ((5,5)-generalized Stirling2).
|
|
LINKS
|
W. Lang, First 5 rows.
|
|
FORMULA
|
G.f. for m-th column (without leading zeros and m>=1) is 1/product(1-fallfac(r+4, 5)*x, r=1..m) with fallfac(n, k) := A008279(n, k) (falling factorials).
a(n, m)=sum(A090435(m, p)*fallfac(p, 5)^(n-m), p=1..m)/D(m) if n>=m>=1 else 0; with D(m) := A090436(m).
|
|
EXAMPLE
|
[1]; [120,1]; [14400,840,1]; [1728000,619200,3360,1]; ...
|
|
CROSSREFS
|
The column sequences (without leading zeros) are powers of 120, etc.
Sequence in context: A069328 A020546 A073836 this_sequence A062829 A062690 A127148
Adjacent sequences: A090214 A090215 A090216 this_sequence A090218 A090219 A090220
|
|
KEYWORD
|
nonn,easy,tabl
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Dec 01 2003
|
|
|
Search completed in 0.002 seconds
|
