OFFSET
6,2
LINKS
T. D. Noe, Table of n, a(n) for n = 6..1000
S. Butler, P. Karasik, A note on nested sums, J. Int. Seq. 13 (2010), 10.4.4, page 5.
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = sum(A008517(5, m+1)*binomial(n+5-m, 2*5), m=0..4) from the o.g.f. See p. 257 eq. (6.43) of the R. L. Graham et al. book quoted in A008517.
O.g.f.: x*sum(A008517(5, m+1)*x^m, m=0..4)/(1-x)^11 with the fifth row [1, 52, 328, 444, 120] of the second-order Eulerian triangle A008517.
E.g.f. with offset n=-4: exp(x)*sum(A112493(5, m)*(x^(m+5))/(m+5)!, m=0..5) with the k=5 row [1, 57, 546, 1750, 2205, 945] of triangle A112493.
a(n) = sum(A112493(5, m)*binomial(n+4, 5+m), m=0..5) from the e.g.f. (coefficients from A112493(5, m) are [1, 57, 546, 1750, 2205, 945]).
With an offset of 1 the o.g.f. is D^5(x/(1-x)), where D is the operator x/(1-x)*d/dx. - Peter Bala, Jul 02 2012
G.f.: x^6*(1 + 52*x + 328*x^2 + 444*x^3 + 120*x^4) / (1 - x)^11. - Colin Barker, Nov 04 2017
MATHEMATICA
Table[StirlingS2[n, n-5], {n, 6, 100}] (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)
PROG
(Sage) [stirling_number2(n, n-5) for n in range(6, 30)] # Zerinvary Lajos, May 16 2009
(PARI) for(n=6, 50, print1(stirling(n, n-5, 2), ", ")) \\ G. C. Greubel, Oct 22 2017
(PARI) Vec(x^6*(1 + 52*x + 328*x^2 + 444*x^3 + 120*x^4) / (1 - x)^11 + O(x^40)) \\ Colin Barker, Nov 04 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 14 2005
STATUS
approved