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%I #17 Oct 02 2022 15:36:29
%S 1,1,2,3,5,7,11,15,22,29,41,54,74,96,128,165,216,275,355,448,571,715,
%T 901,1120,1399,1727,2139,2625,3228,3938,4812,5840,7094,8568,10352,
%U 12447,14967,17919,21450,25581,30496,36234,43031,50951,60292
%N Number of partitions of n that do not contain 9 as a part.
%F G.f.: (1-x^9) Product_{m>0} 1/(1-x^m).
%F a(n) = A000041(n)-A000041(n-9).
%F a(n) ~ 3*Pi * exp(sqrt(2*n/3)*Pi) / (4*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 9*Pi/(2*sqrt(6)))/sqrt(n) + (109/8 + 9/(2*Pi^2) + 15769*Pi^2/6912)/n). - _Vaclav Kotesovec_, Nov 04 2016
%p A41:= n-> `if`(n<0, 0, combinat[numbpart](n)):
%p a:= n-> A41(n) -A41(n-9):
%p seq(a(n), n=0..50);
%t Table[Count[IntegerPartitions[n],_?(FreeQ[#,9]&)],{n,0,50}] (* _Harvey P. Dale_, Oct 02 2022 *)
%Y 9th column of A175788. Cf. A000041, A027336, A027337-A027344.
%K nonn
%O 0,3
%A _Clark Kimberling_
%E Edited by _Alois P. Heinz_, Dec 04 2010
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