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A027341 Number of partitions of n that do not contain 7 as a part. 1
1, 1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 51, 70, 90, 120, 154, 201, 255, 329, 413, 526, 657, 826, 1024, 1278, 1573, 1946, 2383, 2926, 3563, 4349, 5267, 6391, 7707, 9300, 11165, 13412, 16033, 19173, 22836, 27195, 32273, 38291, 45284, 53538, 63119, 74373 (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^7) Product_{m>0} 1/(1-x^m).

a(n)=A000041(n)-A000041(n-7).

a(n) ~ 7*Pi * exp(sqrt(2*n/3)*Pi) / (12*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 7*Pi/(2*sqrt(6)))/sqrt(n) + (85/8 + 9/(2*Pi^2) + 9577*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 04 2016

PROG

(PARI) a(n)=if(n<0, 0, polcoeff((1-x^7)/eta(x+x*O(x^n)), n))

CROSSREFS

Column 7 of A175788.

Sequence in context: A035985 A035995 A036006 * A262371 A184642 A094252

Adjacent sequences:  A027338 A027339 A027340 * A027342 A027343 A027344

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Benoit Cloitre, Dec 10 2002

STATUS

approved

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Last modified June 7 02:46 EDT 2020. Contains 334836 sequences. (Running on oeis4.)