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%I #24 Dec 02 2020 08:18:59
%S 1,55,1705,39325,752752,12662650,193754990,2758334150,37112163803,
%T 477297033785,5917584964655,71187132291275,835143799377954,
%U 9593401297313460,108254081784931500,1203163392175387500,13199555372846848005,143197070509423605675
%N Stirling numbers of second kind: 10th column of Stirling2 triangle A008277.
%D See A000771.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (55,-1320,18150,-157773,902055,-3416930,8409500,-12753576,10628640,-3628800).
%F G.f.: x^10/Product_{k=1..10} (1-k*x).
%F E.g.f.: ((exp(x)-1)^10)/10!.
%F 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
%t lst={};Do[f=StirlingS2[n, 10];AppendTo[lst, f], {n, 10, 5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 27 2008 *)
%t 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 *)
%t StirlingS2[Range[10,35],10] (* _Harvey P. Dale_, Nov 07 2020 *)
%Y Cf. A000225, A000392, A000453, A000481, A000770, A000771, A049434, A049447. a(n) = A008277(n, 10).
%K easy,nonn
%O 10,2
%A _Wolfdieter Lang_
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