A049447 Stirling numbers of second kind: 9th column of Stirling2 triangle A008277.

1, 45, 1155, 22275, 359502, 5135130, 67128490, 820784250, 9528822303, 106175395755, 1144614626805, 12011282644725, 123272476465204, 1241963303533920, 12320068811796900, 120622574326072500, 1167921451092973005, 11201516780955125625, 106563273280541795575

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