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

6,3

Links

T. D. Noe, Table of n, a(n) for n = 6..1000

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

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

Mathematica

Table[StirlingS2[n, n-6], {n, 6, 30}] (* Harvey P. Dale, Sep 21 2011 *)

Prog

(Sage) [stirling_number2(n, n-6) for n in range(6, 28)] # Zerinvary Lajos, May 16 2009
(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
(PARI) for(n=6, 50, print1(stirling(n, n-6, 2), ", ")) \\ G. C. Greubel, Oct 23 2017

Crossrefs

Cf. A008517, A112493.

Sequence in context: A321546 A345458 A008398 * A114535 A215611 A176357

Adjacent sequences: A144966 A144967 A144968 * A144970 A144971 A144972

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 27 2008

Status

approved