A144969 Stirling numbers of second kind S(n,n-6).
0, 1, 127, 3025, 34105, 246730, 1323652, 5715424, 20912320, 67128490, 193754990, 512060978, 1256328866, 2892439160, 6302524580, 13087462580, 26046574004, 49916988803, 92484925445, 166218969675, 290622864675, 495564056130, 825906183960, 1347860993700
Offset: 6
Links
- T. D. Noe, Table of n, a(n) for n = 6..1000
- Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 29.
- Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
Programs
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Mathematica
Table[StirlingS2[n,n-6], {n,6,30}] (* Harvey P. Dale, Sep 21 2011 *) -
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
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PARI
for(n=6,50, print1(stirling(n,n-6,2), ", ")) \\ G. C. Greubel, Oct 23 2017
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Sage
[stirling_number2(n,n-6) for n in range(6, 28)] # Zerinvary Lajos, May 16 2009
Formula
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
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