OFFSET
0,15
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{d|2*n} mu(d)*([x^n] B(2*n/d, x)) for n > 0, where B(m,x) = 1/(Product_{d|m} 1 - x^d). - Andrew Howroyd, Feb 12 2022
EXAMPLE
The a(10) = 1 through a(20) = 10 partitions (A = 10) (empty columns not shown):
(541) (831) (7421) (A32) (9432) (A82)
(74111) (5532) (9441) (8552)
(6522) (94221) (A811)
(6531) (94311) (85421)
(A311) (942111) (85511)
(53322) (9411111) (852221)
(65211) (854111)
(532221) (8522111)
(533211) (85211111)
(651111) (851111111)
(5322111)
(53211111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], LCM@@#==2*n&]], {n, 30}]
PROG
(PARI)
b(m, n)={my(d=divisors(m)); polcoef(1/prod(i=1, #d, 1 - x^d[i] + O(x*x^n)), n)}
a(n)={if(n<1, 0, sumdiv(2*n, d, moebius(d)*b(2*n/d, n)))} \\ Andrew Howroyd, Oct 09 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 25 2019
STATUS
approved