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A230197
The number of multinomial coefficients over partitions with value equal to 7.
5
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 4, 4, 4, 3, 4, 4, 5, 5, 5, 5, 4, 5, 6, 6, 6, 6, 6, 5, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 8, 9, 9, 9, 9, 10, 10, 9, 10, 10, 10, 11, 11, 11, 10, 11, 11, 12, 12, 12
OFFSET
1,13
COMMENTS
The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=7 and t_1+2*t_2+...+n*t_n=n, where t_1, t_2, ... , t_n are nonnegative integers.
FORMULA
a(n) = floor((n-1)*(1/6))+floor((n-1)*(1/7))-floor((1/7)*n).
G.f.: x^8*(2*x^5+x^4+x^3+x^2+x+1) / ((x-1)^2*(x+1)*(x^2-x+1)*(x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)). - Colin Barker, Oct 14 2013
EXAMPLE
The number 19 has three partitions such that a(19)=3: 1+1+1+1+1+1+13, 1+3+3+3+3+3+3 and 2+2+2+2+2+2+7.
MAPLE
seq(floor((n-1)*(1/6))+floor((n-1)*(1/7))-floor((1/7)*n), n=1..75)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Oct 11 2013
STATUS
approved