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 A032180 Number of ways to partition n labeled elements into 6 pie slices. 7
 120, 2520, 31920, 317520, 2739240, 21538440, 158838240, 1118557440, 7612364760, 50483192760, 328191186960, 2100689987760, 13282470124680, 83169792213480, 516729467446080, 3190281535536480, 19596640721427000, 119876382958008600 (list; graph; refs; listen; history; text; internal format)
 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*Stirling2[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 Cf. A000770, A008277, A000225, A028243, A028244, A028245. Sequence in context: A038745 A267839 A220050 * A000553 A126232 A105943 Adjacent sequences:  A032177 A032178 A032179 * A032181 A032182 A032183 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vincenzo Librandi Oct 19 2013 STATUS approved

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Last modified August 21 14:53 EDT 2018. Contains 313954 sequences. (Running on oeis4.)