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

25,2

Links

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

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).

Mathematica

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

Crossrefs

Column k=9 of A209318.

Sequence in context: A217741 A074134 A056178 * A227566 A280421 A369425

Adjacent sequences: A320594 A320595 A320596 * A320598 A320599 A320600

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 16 2018

Status

approved