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

Author

Wolfdieter Lang

Keywords

• easy
• nonn

References

• See A000771.

Crossrefs

Cf. A000225, A000392, A000453, A000481, A000770, A000771, A049434.

Programs

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 *)

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