A027341 Number of partitions of n that do not contain 7 as a part.

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

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Column 7 of A175788.

Programs

Mathematica

Table[Count[IntegerPartitions[n],?(FreeQ[#,7]&)],{n,0,50}] (* _Harvey P. Dale, Sep 26 2021 *)

PARI

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

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

Extensions

More terms from Benoit Cloitre, Dec 10 2002