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A230167
The number of multinomial coefficients over partitions with value equal to 6.
5
0, 0, 0, 0, 0, 2, 2, 4, 4, 7, 7, 10, 10, 15, 14, 20, 19, 25, 24, 31, 31, 39, 37, 45, 44, 55, 53, 63, 61, 72, 71, 83, 81, 94, 91, 105, 103, 118, 115, 130, 128, 144, 141, 158, 155, 174, 170, 188, 185, 205, 202, 222, 218, 239, 235, 258, 254, 277, 272, 295, 292, 317, 312, 337
OFFSET
1,6
COMMENTS
The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=6 and t_1+2*t_2+...+n*t_n=n, where t_1, t_2, ... , t_n are nonnegative integers.
FORMULA
a(n) = floor((1/12)*(n-3)^2)+floor((n-1)*(1/5))+((1+(-1)^n)*(1/2))*floor((n-2)*(1/4)).
G.f.: x^6*(2*x^9-2*x^6-3*x^5-5*x^4-4*x^3-4*x^2-2*x-2) / ((x-1)^3*(x+1)^2*(x^2-x+1)*(x^2+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Oct 15 2013
EXAMPLE
The number 8 has four partitions such that a(8)=6: 1+1+1+1+1+3, 1+1+3+3, 1+2+5 and 1+3+4.
MAPLE
seq(floor((1/12)*(n-3)^2)+floor((n-1)*(1/5))+((1+(-1)^n)*(1/2))*floor((n-2)*(1/4)), n=1..50)
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Oct 11 2013
EXTENSIONS
More terms from Colin Barker, Mar 06 2014
STATUS
approved