%I #18 Feb 10 2024 09:22:59
%S 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,
%T 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,
%U 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
%N The number of multinomial coefficients over partitions with value equal to 9.
%C 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.
%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,-1).
%F a(n) = floor((n-1)*(1/8))+floor((n-1)*(1/9))-floor((1/9)*n).
%F 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
%e 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.
%p seq(floor((n-1)*(1/8))+floor((n-1)*(1/9))-floor((1/9)*n)), n=1..99)
%t 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 *)
%Y A230128, A230149, A230167, A230197, A230198, A230258.
%K nonn,easy
%O 1,17
%A _Mircea Merca_, Oct 14 2013
%E Typos in formula and Maple code fixed by _Colin Barker_, Mar 06 2014
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