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A244998
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Number of ways for five teams of a World Cup football group to each have n goals for and n goals against.
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1
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1, 44, 870, 9480, 68290, 365936, 1573374, 5709120, 18107760, 51488800, 133748186, 321979164, 726436425, 1549758640, 3148837580, 6129352176, 11486265339, 20807609460, 36563769670, 62510325680, 104239453956, 169923049824, 271300238650, 424972948400
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).
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FORMULA
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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
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MAPLE
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(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:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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