OFFSET
1,2
COMMENTS
Equals to: sum of different possible product of nesting levels in n pairs of parentheses.
LINKS
Using your Head is Permitted, Parenthesis Values, November 2013 riddle.
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, the sum of other values is A000670(5)-1*1*2*3*4=517.
PROG
(Python)
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]]))
[sum(set(j[0] for j in i)) for i in k]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jack Zhang, Sep 10 2020
STATUS
approved