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A027340 Number of partitions of n that do not contain 6 as a part. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..46.

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

PROG

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

CROSSREFS

Column 6 of A175788.

Sequence in context: A035994 A036005 A104503 * A000701 A123975 A321728

Adjacent sequences:  A027337 A027338 A027339 * A027341 A027342 A027343

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Benoit Cloitre, Dec 10 2002

STATUS

approved

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Last modified June 3 05:29 EDT 2020. Contains 334798 sequences. (Running on oeis4.)