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A320597 Number of partitions of n with nine parts in which no part occurs more than twice. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A018141

Adjacent sequences: A320594 A320595 A320596 * A320598 A320599 A320600

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Oct 16 2018

STATUS

approved

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Last modified February 3 18:43 EST 2023. Contains 360044 sequences. (Running on oeis4.)