OFFSET
0,5
LINKS
J. Huh and B. Kim, The number of equivalence classes arising from partition involutions, Int. J. Number Theory, 16 (2020), 925-939.
FORMULA
G.f.: 1/2*(Product_{n>=1} (1-q^(2*n-1))/(1-q^(2*n)) + Product_{n>=1} (1+q^(8*n-7))*(1-q^(8*n-5))*(1-q^(8*n-3))*(1+q^(8*n-1))/((1-q^(8*n-6))*(1-q^(8*n-4))*(1-q^(8*n-2))*(1+q^(8*n)))).
EXAMPLE
a(8) = 6, the relevant partitions of 8 without repeated odd parts being [7,1], [6,2], [5,3], [4,4], [4,2,2], [2,2,2,2].
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeremy Lovejoy, Jul 02 2020
STATUS
approved