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A230257
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The number of multinomial coefficients over partitions with value equal to 9.
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5
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 6, 6, 6, 6, 6, 5, 6, 6, 7, 7, 7, 7, 7, 7, 6, 7, 8, 8, 8, 8, 8, 8, 8, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 10, 11, 11, 11, 11, 11, 11, 12, 12, 11
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OFFSET
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1,17
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COMMENTS
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The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=9 and t_1+2*t_2+...+n*t_n=n, where t_1, t_2, ... , t_n are nonnegative integers.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,-1).
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FORMULA
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a(n) = floor((n-1)*(1/8))+floor((n-1)*(1/9))-floor((1/9)*n).
G.f.: x^10*(2*x^7+x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)^2*(x+1)*(x^2+1)*(x^2+x+1)*(x^4+1)*(x^6+x^3+1)). - Colin Barker, Mar 06 2014
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EXAMPLE
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The number 25 has three partitions such that a(25)=8: 1+1+1+1+1+1+1+1+17, 1+3+3+3+3+3+3+3+3 and 2+2+2+2+2+2+2+2+9.
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MAPLE
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seq(floor((n-1)*(1/8))+floor((n-1)*(1/9))-floor((1/9)*n)), n=1..99)
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2}, 100] (* Harvey P. Dale, Mar 20 2016 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Typos in formula and Maple code fixed by Colin Barker, Mar 06 2014
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STATUS
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approved
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