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A306228 Numerators of the even moments of the standard V-monotone Gaussian distribution (see the reference in 'Links', Section 5). 1
1, 1, 4, 28, 278, 3564, 55928, 1037708, 22217720, 539070560, 14616331912, 437960845728, 14370870516352, 512497731949840, 19736969633949568, 816329819676996352, 36089654605723837664, 1698341924904555647808, 84761545323838638225152, 4471847161631552852257472 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

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

Sequence in context: A128318 A032274 A182964 * A178599 A007559 A138208

Adjacent sequences:  A306225 A306226 A306227 * A306229 A306230 A306231

KEYWORD

frac,nonn

AUTHOR

Adrian Dacko, Jan 30 2019

STATUS

approved

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Last modified June 20 21:16 EDT 2021. Contains 345245 sequences. (Running on oeis4.)