OFFSET
1,4
COMMENTS
Inverse Moebius transform of A025147.
Number of uniform (constant multiplicity) partitions of n not containing 1, ranked by the odd terms of A072774. - Gus Wiseman, Dec 01 2023
EXAMPLE
From Gus Wiseman, Dec 01 2023: (Start)
The a(2) = 1 through a(10) = 8 uniform partitions not containing 1:
(2) (3) (4) (5) (6) (7) (8) (9) (10)
(2,2) (3,2) (3,3) (4,3) (4,4) (5,4) (5,5)
(4,2) (5,2) (5,3) (6,3) (6,4)
(2,2,2) (6,2) (7,2) (7,3)
(2,2,2,2) (3,3,3) (8,2)
(4,3,2) (5,3,2)
(3,3,2,2)
(2,2,2,2,2)
(End)
MATHEMATICA
nmax = 56; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k j)), {j, 2, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[Length[Select[IntegerPartitions[n], FreeQ[#, 1]&&SameQ@@Length/@Split[#]&]], {n, 0, 30}] (* Gus Wiseman, Dec 01 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 13 2019
STATUS
approved