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A340772
Number of strictly increasing sequences of n integers 0 < u_1 < ... < u_n such that 1/u_1 + 1/(u_1 + u_2) + ... + 1/(u_1 + ... + u_n) = n/(n+1).
1
1, 1, 2, 5, 24, 276, 21707, 2227892
OFFSET
1,3
EXAMPLE
a(3) = 2 because the sequences (2, 3, 15) and (2, 4, 6) are solutions since 1/2 + 1/5 + 1/20 = 1/2 + 1/6 + 1/12 = 3/4.
PROG
(PARI)
A340772(n, s=n/(n+1), a_min=0, sn=0) = {
if(s<=0, return(0));
if(n==1,
if((floor(1/s)==1/s) && (1/s-sn>a_min), return(1); , return(0); ),
\\ else
my(count);
for(a=max(a_min, floor(1/s)-sn)+1, floor(n/s)-sn, count+=A340772(n-1, s-1/(sn+a), a, sn+a); );
return(count);
);
};
vector(6, n, A340772(n))
CROSSREFS
Sequence in context: A137157 A359810 A025134 * A370066 A076534 A095708
KEYWORD
nonn,more
AUTHOR
François Marques, Jan 20 2021
STATUS
approved