|
| |
|
|
A049447
|
|
Stirling numbers of second kind: 9th column of Stirling2 triangle A008277.
|
|
4
|
|
|
|
1, 45, 1155, 22275, 359502, 5135130, 67128490, 820784250, 9528822303, 106175395755, 1144614626805, 12011282644725, 123272476465204, 1241963303533920, 12320068811796900, 120622574326072500, 1167921451092973005, 11201516780955125625, 106563273280541795575
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
9,2
|
|
|
REFERENCES
|
See A000771.
|
|
|
LINKS
|
Table of n, a(n) for n=9..27.
|
|
|
FORMULA
|
a(n)= A008277(n, 9).
G.f.: x^9/product_{k=1..9} (1-k*x).
E.g.f.: ((exp(x)-1)^9)/9!.
a(n) = det(|s(i+9,j+8)|, 1 <= i,j <= n-9), where s(n,k) are Stirling numbers of the first kind. - Mircea Merca, Apr 06 2013
|
|
|
MATHEMATICA
|
lst={}; Do[f=StirlingS2[n, 9]; AppendTo[lst, f], {n, 9, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)
CoefficientList[Series[1/((1 - x) (1 - 2 x) (1 - 3 x) (1 - 4 x) (1 - 5 x) (1 - 6 x) (1 - 7 x) (1 - 8 x) (1 - 9 x)), {x, 0, 25}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
StirlingS2[Range[9, 30], 9] (* Harvey P. Dale, Dec 12 2022 *)
|
|
|
CROSSREFS
|
Cf. A000225, A000392, A000453, A000481, A000770, A000771, A049434.
Sequence in context: A320363 A140346 A268870 * A327510 A215769 A320822
Adjacent sequences: A049444 A049445 A049446 * A049448 A049449 A049450
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Wolfdieter Lang
|
|
|
STATUS
|
approved
|
| |
|
|
