A049435 Stirling numbers of second kind: 10th column of Stirling2 triangle A008277.

1, 55, 1705, 39325, 752752, 12662650, 193754990, 2758334150, 37112163803, 477297033785, 5917584964655, 71187132291275, 835143799377954, 9593401297313460, 108254081784931500, 1203163392175387500, 13199555372846848005, 143197070509423605675

Offset

10,2

References

See A000771.

Links

Table of n, a(n) for n=10..27.

Index entries for linear recurrences with constant coefficients, signature (55,-1320,18150,-157773,902055,-3416930,8409500,-12753576,10628640,-3628800).

Formula

G.f.: x^10/Product_{k=1..10} (1-k*x).

E.g.f.: ((exp(x)-1)^10)/10!.

a(n) = det(|s(i+10,j+9)|, 1 <= i,j <= n-10), where s(n,k) are Stirling numbers of the first kind. - Mircea Merca, Apr 06 2013

Mathematica

lst={}; Do[f=StirlingS2[n, 10]; AppendTo[lst, f], {n, 10, 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) (1 - 10 x)), {x, 0, 25}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
StirlingS2[Range[10, 35], 10] (* Harvey P. Dale, Nov 07 2020 *)

Crossrefs

Cf. A000225, A000392, A000453, A000481, A000770, A000771, A049434, A049447. a(n) = A008277(n, 10).

Sequence in context: A166844 A077688 A188712 * A327511 A215770 A320823

Adjacent sequences: A049432 A049433 A049434 * A049436 A049437 A049438

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved