OFFSET
1,2
COMMENTS
a(n) is also the number of different possible products of nesting levels in n pairs of parentheses.
EXAMPLE
n=5: possible values are 1*1*1*1*1, 1*1*1*1*2, 1*1*1*2*2, 1*1*1*2*3, 1*1*2*2*2, 1*1*2*2*3, 1*1*2*3*3, 1*1*2*3*4, 1*2*2*2*2, 1*2*2*2*3, 1*2*2*3*3, 1*2*2*3*4, 1*2*3*3*3, 1*2*3*3*4, 1*2*3*4*4, 1*2*3*4*5, but since 1*1*2*3*4=1*2*2*2*3, there are only 15 different values.
PROG
(Python3)
k=[{(1, 1)}]
for i in range(20):
k.append(set([(i[0]*i[1], i[1]) for i in k[-1]])|set([(i[0]*(i[1]+1), i[1]+1) for i in k[-1]]))
[len(set(j[0] for j in i)) for i in k]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jack Zhang, Sep 10 2020
EXTENSIONS
a(31)-a(32) from David A. Corneth, Sep 12 2020
a(33)-a(36) from Bert Dobbelaere, Oct 19 2020
STATUS
approved