OFFSET
0,3
LINKS
Adrian Dacko, V-monotone independence, arXiv:1901.06342 [math.FA], 2019.
Adrian Dacko, Java program.
FORMULA
a(n) = b(n,n+1), where the term b(n,k) is defined recursively as follows:
For any nonnegative integers n and 1 <= k <= n+2, we have
b(n+1, k) = Sum_{m=0..n} Sum_{s=L1(k,m)..L2(k,m)} binomial(k-1,s)*binomial(n+2-k,m+1-s)*(delta(s,0)*b(m,1) + Sum_{r=1..s} b(m,r))*b(n-m,k-s),
where L1(k,m) = max(0, (m+k)-(n+1)), L2(k,m) = min(k-1,m+1), and delta(s,0) is the Kronecker delta (see the referrence in 'Links', Lemma 5.4).
PROG
(Java) // See links.
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Adrian Dacko, Jan 30 2019
STATUS
approved