A320597 Number of partitions of n with nine parts in which no part occurs more than twice.

1, 2, 3, 6, 10, 15, 24, 35, 50, 71, 98, 131, 178, 234, 304, 393, 503, 633, 798, 992, 1225, 1506, 1839, 2226, 2692, 3229, 3856, 4587, 5434, 6400, 7526, 8804, 10266, 11934, 13830, 15964, 18397, 21123, 24192, 27640, 31505, 35805, 40629, 45978, 51928, 58531, 65849

Offset: 25

Author

Alois P. Heinz, Oct 16 2018

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 25..10000

Crossrefs

Column k=9 of A209318.

Programs

Mathematica

Table[Count[IntegerPartitions[n,{9}],?(Max[Length/@Split[#]]<3&)],{n,25,75}] (* _Harvey P. Dale, Nov 10 2022 *)

Formula

G.f.: (x^20-x^19-x^18-x^16+x^14+2*x^11+x^10+x^9+x^8-x^6-x^4-x^3-x-1)*x^25 / ((x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^6+x^3+1) *(x^4+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2+1)^2 *(x^2+x+1)^3 *(x+1)^4 *(x-1)^9).