A049434 Stirling numbers of second kind: 8th column of Stirling2 triangle A008277.

1, 36, 750, 11880, 159027, 1899612, 20912320, 216627840, 2141764053, 20415995028, 189036065010, 1709751003480, 15170932662679, 132511015347084, 1142399079991620, 9741955019900400, 82318282158320505, 690223721118368580, 5749622251945664950

Offset: 8

Author

Wolfdieter Lang

Keywords

• easy
• nonn

References

• See A000771.

Crossrefs

Cf. A000225, A000392, A000453, A000481, A000770, A000771, A049435. a(n)= A008277(n, 8).

Programs

Mathematica

lst={};Do[f=StirlingS2[n, 8];AppendTo[lst, f], {n, 8, 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)), {x, 0, 25}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)

Formula

G.f.: x^8/product_{k=1..8} (1-k*x).

E.g.f.: ((exp(x)-1)^8)/8!.

a(n) = det(|s(i+8,j+7)|, 1 <= i,j <= n-8), where s(n,k) are Stirling numbers of the first kind. - Mircea Merca, Apr 06 2013