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Number of partitions of n that do not contain 6 as a part.
3

%I #14 Nov 04 2016 12:02:28

%S 1,1,2,3,5,7,10,14,20,27,37,49,66,86,113,146,189,241,308,389,492,616,

%T 771,958,1190,1468,1809,2218,2716,3310,4029,4884,5913,7133,8592,10318,

%U 12373,14795,17666,21042,25028,29700,35197,41624,49160,57949,68220

%N Number of partitions of n that do not contain 6 as a part.

%C Also number of partitions of n where no part appears more than five times.

%F G.f.: (1-x^6) Product_{m>0} 1/(1-x^m).

%F a(n) = A000041(n)-A000041(n-6).

%F a(n) ~ Pi * exp(sqrt(2*n/3)*Pi) / (2*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 6*Pi/(2*sqrt(6)))/sqrt(n) + (73/8 + 9/(2*Pi^2) + 7057*Pi^2/6912)/n). - _Vaclav Kotesovec_, Nov 04 2016

%o (PARI) a(n)=if(n<0,0,polcoeff((1-x^6)/eta(x+x*O(x^n)),n))

%Y Column 6 of A175788.

%K nonn

%O 0,3

%A _Clark Kimberling_

%E More terms from _Benoit Cloitre_, Dec 10 2002