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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
Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).
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-François Alcover, Dec 02 2017 *)
CROSSREFS
Sequence in context: A297083 A282994 A295273 * A159948 A183756 A183750
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 09 2014
STATUS
approved

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Last modified July 24 09:48 EDT 2024. Contains 374583 sequences. (Running on oeis4.)