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A058844 Number of ways of placing n labeled balls into 4 indistinguishable boxes with at least 2 balls in each box. 8
105, 1260, 9450, 56980, 302995, 1487200, 6914908, 30950920, 134779645, 575156036, 2417578670, 10046531276, 41388056231, 169371383384, 689568172832, 2796362035104, 11305163394129, 45595968007260, 183557935474290, 737897437077060, 2963015460969915 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,1

LINKS

T. D. Noe, Table of n, a(n) for n=8..200

FORMULA

E.g.f.: ((exp(x) - 1 - x)^4)/4!.

G.f.: x^8*(288*x^6 - 1560*x^5 + 3500*x^4 - 4130*x^3 + 2625*x^2 - 840*x + 105) / ((1 - x)^4*(1 - 2*x)^3*(1 - 3*x)^2*(1 - 4*x)).

a(n) = (4^n-3^(n-1)(4n+12)+2^(n-1)(12+9n+3n^2)-4n^3-8n-4)/24. - David Wasserman, Jun 06 2007

EXAMPLE

a(8) = 8!/(2!*2!*2!*2!*4!) = 105.

MAPLE

A058844:=n->(4^n-3^(n-1)*(4*n+12)+2^(n-1)*(12+9*n+3*n^2)-4*n^3-8*n-4)/24: seq(A058844(n), n=8..25); # Wesley Ivan Hurt, Oct 28 2014

MATHEMATICA

Table[(4^n - 3^(n - 1) (4 n + 12) + 2^(n - 1) (12 + 9 n + 3 n^2) - 4 n^3 - 8 n - 4)/24, {n, 8, 25}] (* Wesley Ivan Hurt, Oct 28 2014 *)

offset = 8; terms = 21; egf = (Exp[x]-1-x)^4/4!; Drop[CoefficientList[egf + O[x]^(terms+offset), x]*Range[0, terms+offset-1]!, offset] (* Jean-Fran├žois Alcover, May 07 2017 *)

PROG

(MAGMA) [(4^n-3^(n-1)*(4*n+12)+2^(n-1)*(12+9*n+3*n^2)-4*n^3-8*n-4)/24 : n in [8..25]]; // Wesley Ivan Hurt, Oct 28 2014

(PARI) a(n)=(4^n - 3^(n-1)*(4*n+12) + 2^(n-1)*(12+9*n+3*n^2) - 4*n^3 - 8*n - 4)/24 \\ Charles R Greathouse IV, Oct 28 2014

CROSSREFS

Cf. A000247 (2 boxes), A000478 (3 boxes).

Sequence in context: A033593 A297542 A266105 * A297800 A165382 A051015

Adjacent sequences:  A058841 A058842 A058843 * A058845 A058846 A058847

KEYWORD

easy,nonn

AUTHOR

Michael Steyer, Dec 02 2000

EXTENSIONS

More terms from James A. Sellers, Dec 06 2000

STATUS

approved

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Last modified November 21 11:43 EST 2018. Contains 317447 sequences. (Running on oeis4.)