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A078999
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Coefficients A_n for the s=4 tennis ball problem.
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2
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1, 14, 156, 1622, 16347, 161970, 1588176, 15465222, 149866020, 1447117432, 13935821924, 133921143546, 1284811863298, 12309517103724, 117803253946752, 1126336913303526, 10760609522499660, 102733711144434216, 980250448431562864, 9348504508099893272
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OFFSET
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0,2
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REFERENCES
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D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344 (A_n for s=4).
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LINKS
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FORMULA
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Conjecture D-finite with recurrence -729*(3*n+2)*(447758283*n-407746117) *(3*n+4) *(n+1)*a(n) +216*(182049960672*n^4 +605681769096*n^3 -358290749358*n^2 -265170598015*n -38328134998)*a(n-1) +1536 *(30350980224*n^4 -947048676672*n^3 +1377152586736*n^2 -569141632910*n +54868443093)*a(n-2) -131072*(4*n-5) *(351198196*n -151260957) *(4*n-7) *(2*n-3)*a(n-3)=0. - R. J. Mathar, Mar 31 2023
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MAPLE
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FussArea := proc(s, n)
local a, i, j ;
a := binomial((s+1)*n, n)*n/(s*n+1) ; ;
add(j *(n-j) *binomial((s+1)*j, j) *binomial((s+1)*(n-j), n-j) /(s*j+1) /(s*(n-j)+1), j=0..n) ;
a := a+binomial(s+1, 2)*% ;
for j from 0 to n-1 do
for i from 0 to j do
i*(j-i) /(s*i+1) /(s*(j-i)+1) /(n-j)
*binomial((s+1)*i, i) *binomial((s+1)*(j-i), j-i)
*binomial((s+1)*(n-j)-2, n-1-j) ;
a := a-%*binomial(s+1, 2) ;
end do:
end do:
a ;
end proc:
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MATHEMATICA
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FussArea[s_, n_] := Module[{a, i, j, pc}, a = Binomial[(s + 1)*n, n]*n/(s*n + 1); pc = Sum[j*(n - j)*Binomial[(s + 1)*j, j]*Binomial[(s + 1)*(n - j), n - j]/(s*j + 1)/(s*(n - j) + 1), {j, 0, n}]; a = a + Binomial[s + 1, 2]*pc; For[j = 0, j <= n - 1 , j++, For[i = 0, i <= j, i++, pc = i*(j - i)/(s*i + 1)/(s*(j - i) + 1)/(n - j)*Binomial[(s + 1)*i, i]* Binomial[(s + 1)*(j - i), j - i]*Binomial[(s + 1)*(n - j) - 2, n - 1 - j]; a = a - pc*Binomial[s + 1, 2]; ]]; a];
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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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