OFFSET
0,3
COMMENTS
Number of partitions of n such that the number of parts is a power of 2.
Also number of partitions of n such that the largest part is a power of 2.
EXAMPLE
a(6) = 6 because we have [6], [5, 1], [4, 2], [3, 3], [3, 1, 1, 1] and [2, 2, 1, 1] (see the first comment) or [4, 2], [4, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1] (see the second comment).
MATHEMATICA
nmax = 52; CoefficientList[Series[Sum[x^(2^k)/Product[1 - x^j, {j, 1, 2^k}], {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 05 2020
STATUS
approved