%I #19 Jun 13 2015 00:54:46

%S 0,0,0,0,0,1,1,1,2,1,2,2,3,3,2,3,4,4,4,3,5,5,5,5,5,6,6,6,7,6,7,7,8,8,

%T 7,8,9,9,9,8,10,10,10,10,10,11,11,11,12,11,12,12,13,13,12,13,14,14,14,

%U 13,15,15,15,15,15,16,16,16,17,16,17,17,18,18,17

%N The number of multinomial coefficients over partitions with value equal to 5.

%C The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=5 and t_1+2*t_2+...+n*t_n=n, where t_1, t_2, ... , t_n are nonnegative integers.

%H Vincenzo Librandi, <a href="/A230149/b230149.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,1,0,0,0,-1).

%F a(n) = floor((1/4)*(n-1)) +floor((1/5)*(n-1)) -floor((1/5)*n).

%F a(n) = a(n-4) + a(n-5) - a(n-9). - _Charles R Greathouse IV_, Oct 11 2013

%F G.f.: x^6*(1+x+x^2+2*x^3)/((1+x)*(1-x)^2*(1+x^2)*(1+x+x^2+x^3+x^4)). - _Bruno Berselli_, Oct 11 2013

%e The number 11 has two partitions such that a(10)=5: 1+1+1+1+7 and 2+2+2+2+3.

%p seq(floor((n-1)*(1/4))+floor((n-1)*(1/5))-floor((1/5)*n), n=1..50)

%t CoefficientList[Series[x^5 (1 + x + x^2 + 2 x^3)/((1 + x) (1 - x)^2 (1 + x^2) (1 + x + x^2 + x^3 + x^4)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Oct 11 2013 *)

%o (PARI) a(n)=(n-1)\4-(n%5==0) \\ _Charles R Greathouse IV_, Oct 11 2013

%K nonn,easy

%O 1,9

%A _Mircea Merca_, Oct 11 2013

%E More terms from _Bruno Berselli_, Oct 11 2013

%E G.f. adapted to the offset from _Vincenzo Librandi_, Oct 11 2013