A027340 Number of partitions of n that do not contain 6 as a part.

1, 1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 49, 66, 86, 113, 146, 189, 241, 308, 389, 492, 616, 771, 958, 1190, 1468, 1809, 2218, 2716, 3310, 4029, 4884, 5913, 7133, 8592, 10318, 12373, 14795, 17666, 21042, 25028, 29700, 35197, 41624, 49160, 57949, 68220

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

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

Crossrefs

Column 6 of A175788.

Programs

PARI

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

Formula

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

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

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

Extensions

More terms from Benoit Cloitre, Dec 10 2002