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Stirling numbers of second kind S(n,n-6).
4

%I #31 Dec 07 2019 12:18:25

%S 0,1,127,3025,34105,246730,1323652,5715424,20912320,67128490,

%T 193754990,512060978,1256328866,2892439160,6302524580,13087462580,

%U 26046574004,49916988803,92484925445,166218969675,290622864675,495564056130,825906183960,1347860993700

%N Stirling numbers of second kind S(n,n-6).

%H T. D. Noe, <a href="/A144969/b144969.txt">Table of n, a(n) for n = 6..1000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

%F With an offset of 1 the o.g.f. is D^6(x/(1-x)), where D is the operator x/(1-x)*d/dx. See A008517. For the e.g.f. see A112493. - _Peter Bala_, Jul 02 2012

%F G.f.: x^7*(720*x^5 +3708*x^4 +4400*x^3 +1452*x^2 +114*x +1)/(1-x-)^13. - _Colin Barker_, Oct 28 2014

%t Table[StirlingS2[n,n-6], {n,6,30}] (* _Harvey P. Dale_, Sep 21 2011 *)

%o (Sage) [stirling_number2(n,n-6) for n in range(6, 28)] # _Zerinvary Lajos_, May 16 2009

%o (PARI) concat(0, Vec(x^7*(720*x^5 +3708*x^4 +4400*x^3 +1452*x^2 +114*x +1 )/(1-x)^13 + O(x^100))) \\ _Colin Barker_, Oct 28 2014

%o (PARI) for(n=6,50, print1(stirling(n,n-6,2), ", ")) \\ _G. C. Greubel_, Oct 23 2017

%Y Cf. A008517, A112493.

%K nonn,easy

%O 6,3

%A _Vladimir Joseph Stephan Orlovsky_, Sep 27 2008