OFFSET
0,7
FORMULA
G.f.: Sum_{n>=1} q^(n*(3*n-1)/2)*Product_{k=1..n-1} (1+q^k)/(1-q^k). - Jeremy Lovejoy, Sep 26 2022
EXAMPLE
The a(11) = 2 through a(17) = 12 partitions (A-F = 10..15):
(92) (A2) (B2) (C2) (D2) (E2) (F2)
(821) (543) (643) (653) (753) (763) (863)
(921) (A21) (743) (843) (853) (953)
(5431) (B21) (C21) (943) (A43)
(5432) (6432) (D21) (E21)
(6431) (6531) (6532) (7532)
(7431) (7432) (7631)
(54321) (7531) (8432)
(8431) (8531)
(64321) (9431)
(65321)
(74321)
MATHEMATICA
pq[y_]:=Length[Select[Range[Length[y]], #==y[[#]]&]];
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&pq[#]>0&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2022
STATUS
approved