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A027338 Number of partitions of n that do not contain 4 as a part. 3

%I

%S 1,1,2,3,4,6,9,12,17,23,31,41,55,71,93,120,154,196,250,314,396,495,

%T 617,765,948,1166,1434,1755,2143,2607,3168,3832,4631,5578,6706,8041,

%U 9628,11494,13705,16302,19361,22946,27159,32076,37837,44551,52384,61493

%N Number of partitions of n that do not contain 4 as a part.

%F G.f.: (1-x^4) Product_{m>0} 1/(1-x^m).

%F a(n) = A000041(n)-A000041(n-4).

%F a(n) ~ Pi * exp(sqrt(2*n/3)*Pi) / (3*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 4*Pi/(2*sqrt(6)))/sqrt(n) + (49/8 + 9/(2*Pi^2) + 3169*Pi^2/6912)/n). - _Vaclav Kotesovec_, Nov 04 2016

%o (PARI) a(n)=if(n<0,0,polcoeff((1-x^4)/eta(x+x*O(x^n)),n))

%Y Column 4 of A175788.

%K nonn

%O 0,3

%A _Clark Kimberling_

%E More terms from _Benoit Cloitre_, Dec 10 2002

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)