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Numerators of the even moments of the standard V-monotone Gaussian distribution (see the reference in 'Links', Section 5).
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%I #17 Jul 10 2019 18:40:05

%S 1,1,4,28,278,3564,55928,1037708,22217720,539070560,14616331912,

%T 437960845728,14370870516352,512497731949840,19736969633949568,

%U 816329819676996352,36089654605723837664,1698341924904555647808,84761545323838638225152,4471847161631552852257472

%N Numerators of the even moments of the standard V-monotone Gaussian distribution (see the reference in 'Links', Section 5).

%H Adrian Dacko, <a href="https://arxiv.org/abs/1901.06342">V-monotone independence</a>, arXiv:1901.06342 [math.FA], 2019.

%H Adrian Dacko, <a href="/A306228/a306228.java.txt">Java program</a>.

%F a(n) = b(n,n+1), where the term b(n,k) is defined recursively as follows:

%F For any nonnegative integers n and 1 <= k <= n+2, we have

%F 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),

%F 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).

%o (Java) // See links.

%K frac,nonn

%O 0,3

%A _Adrian Dacko_, Jan 30 2019