The On-Line Encyclopedia of Integer Sequences (OEIS)

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A027339 revision #10

A027339

Number of partitions of n that do not contain 5 as a part.

1, 1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 62, 79, 105, 134, 175, 220, 284, 355, 451, 561, 705, 870, 1085, 1331, 1644, 2008, 2463, 2990, 3646, 4406, 5339, 6425, 7745, 9279, 11135, 13288, 15872, 18875, 22455, 26606, 31537, 37246, 43990, 51796, 60975

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

FORMULA

G.f.: (1-x^5) Product_{m>0} 1/(1-x^m).

a(n)=A000041(n)-A000041(n-5).

a(n) ~ 5*Pi * exp(sqrt(2*n/3)*Pi) / (12*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 5*Pi/(2*sqrt(6)))/sqrt(n) + (61/8 + 9/(2*Pi^2) + 4921*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 04 2016

PROG

(PARI) a(n)=if(n<0, 0, polcoeff((1-x^5)/eta(x+x*O(x^n)), n))

CROSSREFS

Sequence in context: A035983 A035993 A036004 * A039837 A039838 A064173

Adjacent sequences: A027336 A027337 A027338 * A027340 A027341 A027342

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Benoit Cloitre, Dec 10 2002

STATUS

editing