OFFSET
6,1
COMMENTS
For n>=6, a(n) is equal to the number of functions f: {1,2,...,n-1}->{1,2,3,4,5,6} such that Im(f) contains 5 fixed elements. - Aleksandar M. Janjic and Milan Janjic, Feb 27 2007
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 6..1000
C. G. Bower, Transforms (2)
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).
FORMULA
"CIJ[ 6 ]" (necklace, indistinct, labeled, 6 parts) transform of 1, 1, 1, 1...
a(n) = 120*S(n, 6).
From Emeric Deutsch, May 02 2004: (Start)
a(n) = 5*2^(n-1) - 10*3^(n-1) + 10*4^(n-1) - 5^n + 6^(n-1) - 1.
a(n) = 120*A000770(n). (End)
G.f.: 120*x^6/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - Colin Barker, Sep 03 2012
E.g.f.: (Sum_{k=0..6} (-1)^(6-k)*binomial(6,k)*exp(k*x))/6 with a(n) = 0 for n = 0..5. - Wolfdieter Lang, May 03 2017
MAPLE
with (combstruct):ZL:=[S, {S=Sequence(U, card=r), U=Set(Z, card>=1)}, labeled]: seq(count(subs(r=6, ZL), size=m)/6, m=6..21); # Zerinvary Lajos, Mar 08 2008
MATHEMATICA
CoefficientList[Series[120/((x - 1) (2 x - 1) (3 x - 1) (4 x - 1) (5 x - 1) (6 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 19 2013 *)
Table[120*StirlingS2[n, 6], {n, 6, 30}] (* G. C. Greubel, Nov 19 2017 *)
PROG
(Magma) [5*2^(n-1)-10*3^(n-1)+10*4^(n-1)-5^n+6^(n-1)-1: n in [6..30]]; // Vincenzo Librandi, Oct 19 2013
(PARI) for(n=6, 30, print1(120*stirling(n, 6, 2), ", ")) \\ G. C. Greubel, Nov 19 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi Oct 19 2013
STATUS
approved