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A244998 Number of ways for five teams of a World Cup football group to each have n goals for and n goals against. 1
1, 44, 870, 9480, 68290, 365936, 1573374, 5709120, 18107760, 51488800, 133748186, 321979164, 726436425, 1549758640, 3148837580, 6129352176, 11486265339, 20807609460, 36563769670, 62510325680, 104239453956, 169923049824, 271300238650, 424972948400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..23.

Shalosh B. Ekhad, Doron Zeilberger, There are (1/30)(r+1)(r+2)(2r+3)(r^2+3r+5) Ways For the Four Teams of a World Cup Group to Each Have r Goals For and r Goals Against [Thanks to the Soccer Analog of Prop. 4.6.19 of Richard Stanley's (Classic!) EC1], arXiv:1407.1919, 2014.

FORMULA

Shalosh B. Ekhad and Doron Zeilberger give an explicit formula for a(n).

G.f.: ( 1+32*x+408*x^2+1724*x^3+2765*x^4+1724*x^5+408*x^6+32*x^7+x^8 ) / (x-1)^12. - R. J. Mathar, Jan 31 2015

MAPLE

A244998 := proc(n)

    (n+1)*(n+2)*(n+3)/241920 ;

    %*(43*n^8 +688*n^7 +4934*n^6 +20680*n^5 +55907*n^4 +101272*n^3 +123436*n^2 +96240*n +40320) ;

end proc:

MATHEMATICA

LinearRecurrence[{12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1}, {1, 44, 870, 9480, 68290, 365936, 1573374, 5709120, 18107760, 51488800, 133748186, 321979164}, 24] (* Jean-Fran├žois Alcover, Dec 02 2017 *)

CROSSREFS

Sequence in context: A297083 A282994 A295273 * A159948 A183756 A183750

Adjacent sequences:  A244995 A244996 A244997 * A244999 A245000 A245001

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 09 2014

STATUS

approved

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Last modified December 1 12:50 EST 2020. Contains 338833 sequences. (Running on oeis4.)