|
%I #13 Mar 11 2017 13:33:15
%S 1,1,2,3,5,7,11,15,21,29,40,53,72,94,124,161,209,267,343,434,550,691,
%T 867,1079,1344,1661,2051,2520,3091,3773,4602,5587,6774,8185,9874,
%U 11873,14259,17072,20411,24343,28989,34440,40864,48378,57198,67497,79543
%N Number of partitions of n that do not contain 8 as a part.
%F G.f.: (1-x^8) Product_{m>0} 1/(1-x^m).
%F a(n)=A000041(n)-A000041(n-8).
%F a(n) ~ 2*Pi * exp(sqrt(2*n/3)*Pi) / (3*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 8*Pi/(2*sqrt(6)))/sqrt(n) + (97/8 + 9/(2*Pi^2) + 12481*Pi^2/6912)/n). - _Vaclav Kotesovec_, Nov 04 2016
%t Table[Count[IntegerPartitions[n],_?(FreeQ[#,8]&)],{n,0,50}] (* _Harvey P. Dale_, Mar 11 2017 *)
%o (PARI) a(n)=if(n<0,0,polcoeff((1-x^8)/eta(x+x*O(x^n)),n))
%Y Column 8 of A175788.
%K nonn
%O 0,3
%A _Clark Kimberling_
%E More terms from _Benoit Cloitre_, Dec 10 2002
|
