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%I #18 Mar 03 2024 18:58:04
%S 1,44,870,9480,68290,365936,1573374,5709120,18107760,51488800,
%T 133748186,321979164,726436425,1549758640,3148837580,6129352176,
%U 11486265339,20807609460,36563769670,62510325680,104239453956,169923049824,271300238650,424972948400
%N Number of ways for five teams of a World Cup football group to each have n goals for and n goals against.
%H Shalosh B. Ekhad, Doron Zeilberger, <a href="http://arxiv.org/abs/1407.1919">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]</a>, arXiv:1407.1919, 2014.
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).
%F Shalosh B. Ekhad and Doron Zeilberger give an explicit formula for a(n).
%F 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
%p A244998 := proc(n)
%p (n+1)*(n+2)*(n+3)/241920 ;
%p %*(43*n^8 +688*n^7 +4934*n^6 +20680*n^5 +55907*n^4 +101272*n^3 +123436*n^2 +96240*n +40320) ;
%p end proc:
%t 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-François Alcover_, Dec 02 2017 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jul 09 2014
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