A028245 a(n) = 5^(n-1) - 4*4^(n-1) + 6*3^(n-1) - 4*2^(n-1) + 1 (essentially Stirling numbers of second kind).

0, 0, 0, 0, 24, 360, 3360, 25200, 166824, 1020600, 5921520, 33105600, 180204024, 961800840, 5058406080, 26308573200, 135666039624, 694994293080, 3542142833040, 17980946172000, 90990301641624

Offset

1,5

Comments

For n>=2, a(n) is equal to the number of functions f: {1,2,...,n-1}->{1,2,3,4,5} such that Im(f) contains 4 fixed elements. - Aleksandar M. Janjic and Milan Janjic, Mar 08 2007

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1431

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for linear recurrences with constant coefficients, signature (15,-85,225,-274,120).

Formula

a(n) = 24*S(n, 5) = 24*A000481(n). - Emeric Deutsch, May 02 2004

G.f.: -24*x^5/((x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009; checked and corrected by R. J. Mathar, Sep 16 2009

E.g.f.: (Sum_{k=0..5} (-1)^(5-k)*binomial(5,k)*exp(k*x))/5. with a(0) = 0. - Wolfdieter Lang, May 03 2017

Mathematica

24StirlingS2[Range[30], 5] (* Harvey P. Dale, Jun 18 2013 *)
Table[5^(n - 1) - 4*4^(n - 1) + 6*3^(n - 1) - 4*2^(n - 1) + 1, {n, 21}] (* or *)
Rest@ CoefficientList[Series[-24 x^5/((x - 1) (4 x - 1) (3 x - 1) (2 x - 1) (5 x - 1)), {x, 0, 21}], x] (* Michael De Vlieger, Sep 24 2016 *)

Prog

(PARI) for(n=1, 30, print1(24*stirling(n, 5, 2), ", ")) \\ G. C. Greubel, Nov 19 2017
(Magma) [5^(n-1) - 4*4^(n-1) + 6*3^(n-1) - 4*2^(n-1) + 1: n in [1..30]]; // G. C. Greubel, Nov 19 2017

Crossrefs

Cf. A000481, A008277, A163626, A000225, A028243, A028244.

Sequence in context: A137499 A371068 A122813 * A005546 A309843 A081144

Adjacent sequences: A028242 A028243 A028244 * A028246 A028247 A028248

Keyword

nonn,easy

Author

N. J. A. Sloane, Doug McKenzie mckfam4(AT)aol.com

Status

approved